Dissertations / Theses on the topic 'Non-equilibrium and irreversible thermodynamic'

Dans cette thèse nous présentons les résultats sur l'emploi des systèmes Hamiltoniens à port et des systèmes de contact commandés pour la modélisation et la commande de systèmes issus de la Thermodynamique Irréversible. Premièrement nous avons défini une classe de pseudo-systèmes Hamiltoniens à port, appelée systèmes Hamiltoniens à port irréversibles, qui permet de représenter simultanément le premier et le second principe de la Thermodynamique et inclut des modèles d'échangeurs thermiques ou de réacteurs chimiques. Ces systèmes ont été relevés sur l'espace des phases thermodynamiques muni d’une forme de contact, définissant ainsi une classe de systèmes de contact commandés, c'est-à-dire des systèmes commandés non-linéaires définis par des champs de contacts stricts. Deuxièmement, nous avons montré que seul un retour d'état constant préserve la forme de contact et avons alors résolu le problème d'assignation d'une forme de contact en boucle fermée. Ceci a mené à la définition de systèmes de contact entrée-sortie et l'analyse de leur équivalence par retour d'état. Troisièmement, nous avons montré que les champs de contact n'étaient en général pas stables en leur zéros et avons alors traité du problème de la stabilisation sur une sous-variété de Legendre en boucle fermée
This doctoral thesis presents results on the use of port Hamiltonian systems (PHS) and controlled contact systems for modeling and control of irreversible thermodynamic processes. Firstly, Irreversible PHS (IPHS) has been defined as a class of pseudo-port Hamiltonian system that expresses the first and second principle of Thermodynamics and encompasses models of heat exchangers and chemical reactors. These IPHS have been lifted to the complete Thermodynamic Phase Space endowed with a natural contact structure, thereby defining a class of controlled contact systems, i.e. nonlinear control systems defined by strict contact vector fields. Secondly, it has been shown that only a constant control preserves the canonical contact structure, hence a structure preserving feedback necessarily shapes the closed-loop contact form. The conditions for state feedbacks shaping the contact form have been characterized and have lead to the definition of input-output contact systems. Thirdly, it has been shown that strict contact vector fields are in general unstable at their zeros, hence the condition for the the stability in closed-loop has been characterized as stabilization on some closed-loop invariant Legendre submanifolds

A theoretical model describing the motion of a small, fast rare gas atom as it passes over a liquid surface is developed and discussed in detail. A key feature of the model is its reliance on coarse-grained capillary wave and local mode descriptions of the liquid surface. Mathematically, the model is constructed with several concepts from probability and stochastic analysis. The model makes predictions that are quantitative agreement with neon-liquid surface scattering data collected by other research groups. These predictions include the dominance of single, rather than multiple, neon-liquid surface collision dynamics, an average of 60 % energy transfer from a neon atom upon colliding with a non-metallic surface, and an average of 25 % energy transfer upon colliding with a metallic surface. In addition to this work, two other investigations into the gas-liquid interface are discussed. The results of an experimental investigation into the thermodynamics of a gas flux through an aqueous surface are presented, and it is shown that a nitrous oxide flux is mostly due to the presence of a temperature gradient in the gas-liquid interface. Evidence for a reaction between a carbon dioxide flux and an ammonia monolayer on an aqueous surface to produce ammonium carbamate is also found. The second of these is an investigation into the mechanism of bromine production from deliquesced sodium bromide aerosol in the presence of ozone, and involves a sensitivity and uncertainty analysis of the computer aerosol kinetics model MAGIC. It is shown that under dark, non-photolytic conditions, bromine production can be accounted for almost exclusively by a reaction between gas-phase ozone and surface-bound bromide ions. Under photolytic conditions, bromine production instead involves a complicated interplay between various gas-phase and aqueous-phase reactions.

Nous présentons des approches théoriques et numériques pour deux dynamiques irréversibles et parallèles sur des modèles de mécanique statistique. Dans le premier chapitre, nous présentons les résultats théoriques sur un système de particules induite par une chaîne de Markov irréversible, à savoir le TASEP. Permettant des multiples retournements de spin \`à chaque itération, nous définissons un modèle avec une dynamique parallèle appartenant à la famille des PCA et nous dérivons sa mesure stationnaire. Dans ce cadre, nous traitons {\it le problème du blocage}, {\it i.e.} comprendre les effets d’une perturbation localisée dans le taux de transition des particules sur des systèmes irréversibles: le problème du blocage. Dans le deuxième chapitre, nous présentons une version unidimensionnelle du modèle d'Ising avec potentiel de Kac. Nous définissons une PCA avec une interaction asymétrique et nous trouvons sa mesure stationnaire avec condition aux limites périodique.Ensuite, nous prouvons la convergence, dans la limite thermodynamique, de cette mesure stationnaire vers la mesure de Gibbs pour toutes les températures supérieures à la température critique via les estimations de F\"ollmer et le théorème d'unicité de Dobrushin. Dans la seconde partie de la thèse, nous étudions ces deux dynamiques à travers des expériences numériques. Dans le cas du TASEP en exploitant des processeurs graphiques (GPU) et CUDA pour identifier une estimation raisonnable du {temps de m\'elange} et renforcer la conjecture qu’à la fois dans la version, la règle de mise à jour série ou parallèle, le courant peut ne pas être analytique dans l’intensité du blocage autour de la valeur $ \varepsilon = 0 $
In this thesis we present theoretical and numerical approaches for two irreversible and parallel dynamics on one-dimensional statistical mechanics models. In the first chapter we present theoretical results on a particles system driven by an irreversible Markov chain namely the totally asymmetric simple exclusion process (TASEP). Allowing multiples spin-flips in each time-step we define a model with a parallel dynamics that belongs to the family of the probabilistic cellular automata (PCA) and we derive its stationary measure. In this framework we deal with {\it the blockage problem}, {\it i.e.} to understand the effects of a localized perturbation in the transition rates of the particles on irreversible systems: the blockage problem. In the second chapter we present a one-dimensional version of the Ising model with Kac potential. Again we define a PCA dynamics with asymmetric interaction between particles and we find its stationary measure for periodic boundary condition. Then we prove the convergence, in the thermodynamic limit, of such stationary measure to the Gibbs measure for all temperatures above the critical one via F\"ollmer estimates and dobrushin's uniqueness theorem. In the second part of the thesis, we investigate these two dynamics through numerical experiments.In the case of the TASEP we exploit general purpose graphical processors unit (GPGPU) writing a parallel code in CUDA to identify a reasonable {\it mixing time} and reinforce the conjecture that in both version, serial or parallel update rule, the current may be non-analytic in the blockage intensity around the value $\varepsilon = 0$

Quantum information and quantum computing (QIQC) systems, relying on the phenomena of superposition and entanglement, offer the potential for vast improvements in certain computations. A practical QC realization requires maintaining the stored information for time-scales long enough to implement algorithms. One primary cause of information loss is decoherence, i.e., the loss of coherence between two energy levels in a quantum system. This work attributes decoherence to dissipation occurring as the system evolves and uses steepest-entropy-ascent quantum thermodynamics (SEAQT) to predict the evolution of system state. SEAQT asserts that, at any instant of time, the system state evolves such that the rate of system entropy change is maximized while conserving system energy. With this principle, the SEAQT equation of motion is applicable to systems in any state, near or far from stable equilibrium, making SEAQT particularly well suited for predicting the dissipation occurring as quantum algorithms are implemented. In the present research, the dynamics of qubits (quantum-bits) using the SEAQT framework are first examined during common quantum gates (combinations of which form algorithms). This is then extended to modeling a system of multiple qubits implementing Shor's algorithm on a nuclear-magnetic-resonance (NMR) QC. Additionally, the SEAQT framework is used to predict experimentally observed dissipation occurring in a two-qubit NMR QC undergoing a so called ``quenching'' process. In addition, several methods for perturbing the density or so-called ``state'' operator used by the SEAQT equation of motion subject to an arbitrary set of expectation value constraints are presented. These are then used as the basis for randomly generating states used in analyzing the dynamics of entangled, non-interacting systems within SEAQT. Finally, a reservoir interaction model is developed for general quantum systems where each system locally experiences a heat interaction with an external reservoir. This model is then used as the basis for developing a decoherence control scheme, which effectively transfers entropy out of the QIQC system as it is generated, thus, reducing the decoherence. Reservoir interactions are modeled for single qubits and the control scheme is employed in modeling an NMR QC and shown to eliminate nearly all of the noise caused by decoherence/dissipation.
Doctor of Philosophy
Quantum computers (QCs) have the potential to perform certain tasks much more efficiently than today0 s supercomputers. One primary challenge in realizing a practical QC is maintaining the stored information, the loss of which is known as decoherence. This work attributes decoherence to dissipation (a classical analogue being heat generated due to friction) occurring while an algorithm is run on the QC. Standard quantum modeling approaches assume that for any dissipation to occur, the QC must interact with its environment. However, in this work, steepest-entropy-ascent quantum thermodynamics (SEAQT) is used to model the evolution of the QC as it runs an algorithm. SEAQT, developed by Hatsopolous, Gyftopolous, Beretta, and others over the past 40 years, supplements the laws of quantum mechanics with those of thermodynamics and in contrast to the standard quantum approaches does not require the presence of an environment to account for the dissipation which occurs. This work first applies the SEAQT framework to modeling single qubits (quantum bits) to characterize the effect of dissipation on the information stored on the qubit. This is later extended to a nuclear-magnetic-resonance (NMR) QC of 7 qubits. Additionally, SEAQT is used to predict experimentally observed dissipation in a two-qubit NMR QC. Afterwards, several methods for constrained perturbations of a QC0 s state are presented. These methods are then used with SEAQT to analyze the effect of dissipation on the entanglement of two qubits. Finally, a model is derived within the SEAQT framework accounting for a qubit interacting with its environment, which is at a constant temperature. This model is then used to develop a method for limiting the decoherence and shown to significantly lowering the resulting error due to decoherence.

Ziel der vorliegenden Arbeit ist es, das Preisach-Modell bezüglich stochastischer äußerer Felder und temperaturbezogener Aspekte zu untersuchen. Das phänomenologische Preisach-Modell wird oft erfolgreich angewendet, um Systeme mit Hysterese zu beschreiben. Im ersten Teil der Arbeit wird die Antwort des Preisach-Modells auf stochastische äußere Felder untersucht. Hier liegt das Augenmerk hauptsächlich auf der Autokorrelation; sie dient dazu den Einfluss des hysteretischen Gedächtnisses zu quantifizieren. Mit analytischen Methoden wird gezeigt, dass sich ein Langzeitgedächtnis, sichtbar in der Autokorrelation der Systemantwort, entwickeln kann, selbst wenn das treibende Feld unkorreliert ist. Im Anschluss werden diese Resultate, m.H. von Simulationen, auf äußere Felder ausgeweitet, die selbst Korrelationen aufweisen können. Der zweite Teil der Arbeit befasst sich mit dem Einfluss einer endlichen Temperatur auf das Preisach-Modell. Es werden unterschiedliche Methoden besprochen, wie das Nichtgleichgewichtsmodell in seiner mikromagnetischen Interpretation mit Temperatur als Gleichgewichtseigenschaft verknüpft werden kann. Eine Formulierung wird genutzt, um die Magnetisierung von Nickelnanopartikeln in einer Fullerenmatrix zu simulieren und mit Experimenten zu vergleichen. Des Weiteren wird die Relaxationsdynamik des Gedächtnisses des Preisach-Modells bei endlichen Temperaturen untersucht
The aim of this thesis is to investigate the Preisach model in regard to stochastically driving and temperature-related aspects. The Preisach model is a phenomenological model for systems with hysteresis which is often successfully applied. Hysteresis is a widespread phenomenon which is observed in nature and the key feature of certain technological applications. Further, it contributes to phenomena of interest in social science and economics as well. Prominent examples are the magnetization of ferromagnetic materials in an external magnetic field or the adsorption-desorption hysteresis observed in porous media. Hysteresis involves the development of a hysteresis memory, and multistability in the interrelations between external driving fields and system response. In the first part, we mainly investigate the response of Preisach hysteresis models driven by stochastic input processes with regard to autocorrelation functions to quantify the influence of the system’s memory. Using rigorous methods, it is shown that the development of a hysteresis memory is reflected in the possibility of long-time tails in the autocorrelation functions, even for uncorrelated driving fields. In the case of uncorrelated driving, these long-time tails in the autocorrelations of the system’s response are determined only by the tails of the involved densities. They will be observed if there are broad Preisach densities assigning a high weight to elementary loops of large width and narrow input densities such that rare extreme events of the input time series contribute significantly to the output for a long period of time. Afterwards, these results are extended by simulations to driving fields which themselves show correlations. It is shown that the autocorrelation of the output does not decay faster than the autocorrelation of the input process. Further, there is a possibility that long-term memory in the hysteretic response is more pronounced in the case of uncorrelated driving than in the case of correlated driving. The behavior of the output probability distribution at the saturation values is quite universal. It is not affected by the presence of correlations and allows conclusions whether the input density is much more narrow than the Preisach density or not. Moreover, the existence of effective Preisach densities is shown which define equivalence classes of systems of input and Preisach densities which lead to realizations of the same output variable. The asymptotic behavior of an effective Preisach density determines the asymptotic correlation decay of the system’s response in the case of uncorrelated driving. In the second part, temperature-related effects are considered. It is reviewed how the non-equilibrium Preisach model in its micromagnetic picture can be related to temperature within the framework of extended irreversible thermodynamics. The irreversible response of a ferromagnetic material, namely, Nickel nanoparticles in a fullerene matrix, is simulated. The model includes superparamagnetism where ferromagnetism breaks down at temperatures lower than the Curie temperature and the results are compared to experimental data. Furthermore, we adapt known results for the thermal relaxation of the system’s memory in the form of a front propagation in the Preisach plane derived basically from solving a master equation and by the use of a contradictory assumption. A closer look is taken at short time scales which dissolves the contradiction and shows that the known results apply, taking into account the fact that the dividing line propagation starts with an additional delay time depending on the front coordinates in the Preisach plane. Additionally, it is outlined how thermal relaxation behavior in the Preisach model of hysteresis can be studied using a Fokker-Planck equation. The latter is solved analytically in the non-hysteretic limit using eigenfunction methods. The results indicate a change in the relaxation behavior, especially on short time scales

In this research, a first-principles, non-equilibrium thermodynamic-ensemble approach applicable across all temporal and spatial scales is developed based on steepest-entropy-ascent quantum thermodynamics (SEAQT). The SEAQT framework provides an equation of motion consisting of both reversible mechanical dynamics and irreversible relaxation dynamics, which is able to describe the evolution of any state of any system, equilibrium or non-equilibrium. Its key feature is that the irreversible dynamics is based on a gradient dynamics in system state space instead of the microscopic mechanics of more traditional approaches. System energy eigenstructure and density operator (or ensemble probability distribution) describe the system and system thermodynamic state, respectively. Extensive properties (i.e., energy, entropy, and particle number) play a key role in formulating the equation of motion and in describing non-equilibrium state evolutions. All the concepts involved in this framework (i.e., eigentstructure, density operator, and extensive properties) are well defined at all temporal and spatial scales leading to the extremely broad applicability of SEAQT. The focus of the present research is that of developing non-equilibrium thermodynamic models based specifically on the irreversible part of the equation of motion of SEAQT and applying these to the study of pure relaxation processes of systems in non-equilibrium states undergoing chemical reactions and heat and mass diffusion. As part of the theoretical investigation, the new concept of hypo-equilibrium state is introduced and developed. It is able to describe any non-equilibrium state going through a pure relaxation process and is a generalization of the concept of stable equilibrium of equilibrium thermodynamics to the non-equilibrium realm. Using the concept of hypo-equilibrium state, it is shown that non-equilibrium intensive properties can be fundamentally defined throughout the relaxation process. The definition of non-equilibrium intensive properties also relies on various ensemble descriptions of system state. In this research, three SEAQT ensemble descriptions, i.e., the canonical, grand canonical, and isothermal-isobaric, are derived corresponding, respectively, to the definition of temperature, chemical potential, and pressure. To computationally and not just theoretically permit the application of the SEAQT framework across all scales, a density of states method is developed, which is applicable to solving the SEAQT equation of motion for all types of non-equilibrium relaxation processes. In addition, a heterogeneous multiscale method (HMM) algorithm is also applied to extend the application of the SEAQT framework to multiscale modeling. Applications of this framework are given for systems involving chemical kinetics, the heat and mass diffusion of indistinguishable particles, power cycles, and the complex, coupled reaction-diffusion pathways of a solid oxide fuel cell (SOFC) cathode.
Ph. D.

Knowledge of free-energy differences for states of a system provides an essential component in understanding many processes, including solubility, reaction rates, and phase changes. Therefore, the development of efficient, accurate free-energy calculation routines has long been of interest within the field of molecular modelling. Until recently, thermodynamic integration, free-energy perturbation and slow-change techniques were the only approaches available for the calculation of free-energy differences between two states of a system. However, with the discovery of non-equilibrium free-energy relations in the late nineties, new calculation approaches are now possible. This thesis demonstrates the application of these new relations by deriving them from statistical mechanical concepts and applying them to a variety of systems. Although other types of systems are considered, the focus of this work is on the investigation of density changes, as the density of a system is one of its fundamental intrinsic properties, and expansion and compression phenomena are central to many thermodynamic investigations. To investigate the convergence properties of the free-energy calculation methods prior to their application to systems undergoing a density change, a novel transformation between Lennard-Jones systems possessing different potentials is developed and simulations are completed for a variety of transformation parameters. In particular, the accuracy of free-energy calculations as a function of transformation rate is considered, along with a detailed analysis of free-energy convergence as a function of the number of transformations completed.
Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Biomolecular and Physical Sciences
Science, Environment, Engineering and Technology
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Le basi delle Leggi della Termodinamica stanno al centro della costruzione intellettuale della Fisica sin dalla loro prima formulazione alla fine del XIX secolo. A causa della loro centrale rilevanza, questi concetti suscitano ancora dibattiti molto accesi e alimentano feconde discussioni. Dato che questo è vero nel regno della fisica statistica dell'equilibrio - un corpus consolidato di concetti coerenti - la situazione è più instabile nella fisica statistica del non equilibrio, dove i dibattiti fondazionali sono ancora in corso. Questo stato di cose motiva lo studio dei fondamenti teorici e matematici della Fisica Statistica del Non Equilibrio. Oltre agli affascinanti aspetti scientifici, tali studi sono resi necessari da necessità tecnologiche: le bio- nano- tecnologie operano ad una scala in cui i confini tra macroscopico e microscopico sono sfumati; per di più in questi dispositivi il non equilibrio è la regola e non l'eccezione. Per tutti questi motivi, proponiamo la Teoria della Funzione di Dissipazione come base candidata per porre le basi teoriche e matematiche della Fisica Statistica del Non Equilibrio tramite una teoria della risposta non perturbativa.
The foundations of the Laws of Thermodynamics stand in center of the intellectual building of Physics since their early formulation in late XIX century. Because of their central relevance, these concepts still spark flaming debates and propel profound discussions. Given that this is true in the realm of Equilibrium Statistical Physics -- an established corpus of coherent concepts -- the situation is even more volatile in Non Equilibrium Statistical Physics, where foundational debates are still going on. This state of things motivates the study of the theoretical and mathematical foundations of Non Equilibrium Statistical Physics. Besides the fascinating scientific aspects, such studies are made necessary by technological urgencies: bio- nano- technologies operate at a scale in which boundaries between macroscopic and microscopic are blurred, plus in these devices non equilibrium is the rule and not the exception. For all these reasons, we propose Dissipation Function Theory as a candidate base to lay the theoretical and mathematical foundations of Non Equilibrium Statistical Physics via a non perturbative response theory.

Le travail présenté dans cette thèse porte sur la modélisation et la commande d'un système thermodynamique non linéaire de dimension infinie, le réacteur tubulaire. Nous abordons le problème de commande sur ce système non linéaire en nous appuyant sur les propriétés thermodynamiques du procédé. Cette approche nécessite l'utilisation d'un modèle ayant comme variables d'état les variables extensives thermodynamiques classiques. Nous utilisons la fonction de disponibilité thermodynamique ainsi qu'une autre fonction déduite de la précédente, la disponibilité réduite, comme fonction de Lyapunov candidate pour résoudre le problème de stabilisation du réacteur autour d'un profil d'équilibre en utilisant comme commande distribuée la température de la double enveloppe. Des simulations illustrent ces résultats ainsi que l'efficacité des commandes en présence de perturbations. Nous nous intéressons aussi à la représentation hamiltonienne à port des systèmes irréversibles de dimension infinie. La structure de Stokes-Dirac pour un modèle réaction diffusion est obtenue en étendant les vecteurs de variables de flux et d'effort. Nous présentons cette démarche pour les équations du système réaction-diffusion en prenant premièrement l'énergie interne comme Hamiltonien puis deuxièmement l'opposé de l'entropie. Nous montrons dans les deux cas qu'en utilisant une extension des couples de variables effort-flux thermodynamiques classiques nous obtenons une structure de Stokes-Dirac. Enfin nous donnons quelques résultats aboutissant à une représentation pseudo hamiltonienne. Enfin nous abordons le problème de commande à la frontière. L'objectif est d'étudier l'existence de solutions associées à un modèle linéarisé de réacteur tubulaire complet commandé à la frontière
The main objective of this thesis consists to investigate the problem of modelling and control of a nonlinear parameter distributed thermodynamic system : the tubular reactor. We address the control problem of this non linear system relying on the thermodynamic properties of the process. This approach requires to use the classical extensive variables as the state variables. We use the thermodynamic availability as well as the reduced thermodynamic availability (this function is formed from some terms of the thermodynamic availabilty) as Lyapunov functions in order to asymptotically stabilize the tubular reactor aroud a steady profile. The distributed temperature of the jacket is the control variable. Some simulations illustrate these results as well as the eficiency of the control in presence of perturbations. Next we study the Port Hamiltonian representation of irreversible infinite dimensional systems. We propose a Stokes-Dirac structure of a reaction-diffusion system by means of the extension of the vectors of the flux and effort variables. We illustrate this approach on the example of the reaction-diffusion system. For this latter we use the internal energy as well as the opposite of the entropy to obtain Stokes-Dirac structures. We propose also a pseudo-Hamiltonian representation for the two Hamiltonians. Finally we tackle the boundary control problem. The objective is to study the existence of solutions associated to a linearized model of the tubular reactor controlled to the boundary

L'objet de cette thèse est la modélisation et la commande par approche thermodynamique des réacteurs catalytiques triphasiques en mode continu et en mode discontinu. Ce type de réacteur consiste en un système fortement non linéaire, multivariable et siège de réactions exothermiques. Nous utilisons les concepts de la thermodynamique irréversible pour la synthèse de lois de commande stabilisante pour ces deux types de réacteurs chimiques. En effet, la stricte concavité de la fonction d'entropie nous a permis de définir une fonction de stockage qui sert de fonction de Lyapunov candidate : la disponibilité thermodynamique. Nous utilisons cette fonction de disponibilité thermodynamique pour la synthèse de lois de commande stabilisante d'un mini-réacteur catalytique triphasique intensifié continu. Une stratégie de contrôle à deux couches (optimisation et contrôle) est utilisée pour contrôler la température et la concentration du produit à la sortie du réacteur en présence de perturbations à l'entrée du réacteur. Les performances du contrôleur mis en place sont comparées en simulation à celles d'un régulateur PI. Dans certains cas, l'utilisation de la fonction de disponibilité thermodynamique s'avère problématique. Une autre étude effectuée sur cette fonction nous permet de déterminer une nouvelle fonction de Lyapunov : la disponibilité thermique. Nous utilisons par la suite la fonction de disponibilité thermique pour la synthèse de lois de commande stabilisante d'un réacteur catalytique triphasique semi-fermé. Un observateur grand gain est utilisé pour estimer la vitesse de réaction à partir des mesures de la température du milieu réactionnel. Cette estimation est injectée ensuite dans le calcul de la loi de commande mise en place. La robustesse du schéma de contrôle est testée en simulation face à des incertitudes de modélisation, des perturbations et des bruits de mesure.

L’objectif de ce travail est de proposer de nouvelles stratégies de commande non linéaire pour la stabilisation des Réacteurs Parfaitement Agités Continus (RPAC). Pour cela, nous utilisons d’une part, l’approche thermodynamique entropique. Plus précisément, nous utilisons la notion de disponibilité thermodynamique et les propriétés de la thermodynamique irréversible pour définir une fonction de Lyapunov utilisable pour la stabilisation du système en boucle fermée. Nous proposons aussi une fonction disponibilité réduite afin d’obtenir des lois stabilisantes plus performantes en terme de sollicitation des actionneurs. D’autre part, nous proposons une extension du formalisme (pseudo) hamiltonien à ports dissipatifs aux réacteurs chimiques ouverts. Nous montrons que l’Hamiltonien est lié à l’enthalpie libre de Gibbs dans le cas isotherme et à l’ectropie (opposée de l’entropie) dans le cas non isotherme. Par ce formalisme, la dissipation du système représente la production irréversible d’entropie due à la réaction chimique. Nous appliquons ensuite les techniques de commande passive (modelage de l’énergie) pour la synthèse de lois de commande en choisissant la disponibilité thermodynamique comme fonction hamiltonienne à modeler en boucle fermée. Finalement, nous montrons que les commandes synthétisées par l’approche thermodynamique entropique et la formulation pseudo-hamiltonienne sont, dans certains cas, équivalentes. Certaines propriétés relatives à la stabilisation et l’admissibilité des commandes sont aussi considérées. Les développements théoriques sont mis en oeuvre sur des exemples différents de RPAC : un réacteur académique et l’hydrolyse par catalyse acide de l’oxirane-méthanol en glycérine
The goal of this thesis is to propose new nonlinear control strategies for the stabilization of perfectly Continuous Stirred Tank Reactors (CSTR). To achieve this goal, we use on the one hand, the entropic thermodynamic approach. More precisely, we use the thermodynamic availability concept and the properties of irreversible thermodynamics to define a Lyapunov function candidate for the stabilization of the closed loop system. We also propose a reduced availability function to design more efficient feedback laws in term of control variable solicitations. On the other hand, we propose an extension of the (pseudo) Hamiltonian formalism associated to dissipative systems to open chemical reactors. We show that the Hamiltonian is linked to the Gibbs free enthalpy in the isothermal case and to ectropy (opposed to entropy) in the non isothermal case. By this formalism, the dissipation of the system represents the irreversible entropy production due to chemical reaction. The Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) approach is then applied to synthesize feedback laws by choosing the thermodynamic availability as desired closed loop hamiltonian storage function. Finally, we show that feedback laws synthetized by the entropic thermodynamic approach and the pseudo-hamiltonian formulation are equivalent in some cases. Some stabilization properties and the control input admissibility are also considered. Theoretical developments are illustrated on some different CSTR examples : an academic case study and the acid catalyzed hydration of oxirane-methanol to glycerol

Un modèle constitutif complètement couplé est présenté pour l'analyse rigoureuse de la déformation, de l'écoulement de fluides et de transfert de chaleur dans les milieux poreux saturés à double porosité soumis à des chargements thermo-hydro-mécaniques, y compris ceux induisant un non-équilibre thermique local. La phase solide contient deux cavités distinctes: le bloc poreux et le réseau des fissures. Les équations de champs sont obtenues à partir des équations de conservation de la masse, du mouvement et de l'énergie et sont résolues par une approche par élément finis. Le modèle est utilisé pour deux types d'applications: la stabilité d'un puits de forage stimulée thermiquement pour la récupération de pétrole et l'extraction de chaleur dans un réservoir géothermique fracturé. Les différences substantielles, particulièrement de la contrainte effective, soulignent l'influence majeure de la double porosité et du non-équilibre thermique pour prédire le comportement des milieux fracturés.

La modélisation d'un disjoncteur haute tension par un modèle MHD nécessite des banques de données de propriétés du plasma afin de simuler le comportement de l'arc électrique. L'hypothèse d'équilibre thermodynamique local est souvent utilisée afin de calculer ces propriétés. Cependant les conditions d'équilibre ne sont pas remplies près des parois ou des électrodes, ou lors du passage par zéro du courant. Les écarts à l'équilibre (thermique notamment) modifient alors considérablement la chimie et les propriétés du plasma. L'étude de ces propriétés dans ces conditions nécessite alors de supposer que le plasma est à deux températures (2T). Le calcul des propriétés du plasma à 2T fait l'objet de cette thèse. La première partie de cette thèse présente le contexte industriel à l'origine de cette étude. Les hypothèses de base qui sous-tendent l'hypothèse 2T sont ensuite rappelées. Dans cette partie une attention spéciale est portée aux températures caractéristiques de peuplement des modes d'énergies internes. Deux jeux d'hypothèses portant sur ces températures sont utilisés dans ces travaux, et le choix de ces hypothèses est discuté. La deuxième partie de ce travail est consacrée au calcul de composition d'un plasma de SF6-C2F4 à 2T. Ce calcul sera fait avec deux méthodes différentes : la première repose sur la loi d'action de masse étendue à 2T, et la seconde sur un calcul collisionnel-radiatif. Des exemples de composition obtenus avec ces deux méthodes sont présentés. Les hypothèses portant sur les températures de peuplement des niveaux d'énergies internes sont discutées au vu de ces résultats. Le troisième chapitre de cet ouvrage aborde le calcul des propriétés thermodynamiques à 2T du plasma. Les formulations théoriques de chacune de ces propriétés sont d'abord rappelés, et les résultats issus de ces expressions sont ensuite présentés et discutés, pour les deux méthodes de calcul de la composition. Le quatrième chapitre est dédié au calcul des coefficients de transports d'un plasma de SF6-C2F4 à 2T. Cette partie s'appuie sur une étude bibliographique des méthodes de calcul déjà existantes et des données indispensables à l'obtention de ces propriétés (intégrales de collision). Pour chaque propriété (viscosité, conductivité électrique et conductivité thermique) les différentes méthodes de calcul recensées dans la littérature sont comparées. Le choix de la technique de calcul la plus appropriée est réalisé par confrontation de résultats à l'ETL. Une attention toute particulière est portée au calcul de la partie réactive de la conductivité thermique, et une formulation adaptée aux besoins de ce travail est proposée. Les résultats issus de ces expressions sont présentés et discutés suivant la même logique quand dans le chapitre précédent
Modelling a high voltage circuit breaker using a MHD model needs plasma properties databanks to simulate the electric arc behavior. The local thermodynamic equilibrium hypothesis is often used to calculate these properties. However, the equilibrium conditions are not satisfied near the walls or the electrodes, or during the zero crossing of the current. The thermal nonequilibrium considerably modify the chemistry and properties of the plasma. The study of these properties for a 2t plasma is the subject of this thesis. The first part of this thesis presents the industrial context at the origin of this study. Basics assumptions for the 2t hypothesis are then explained. In this section, special attention is given to the temperatures characteristic of the internal energy modes. Two sets of hypotheses concerning these temperatures are used in this work, and the choice of these hypotheses is discussed. The second part of this work is dedicated to the calculation of sf6-c2f4 plasma composition at 2t. This calculation will be done with two different methods: the first is based on the mass action law extended to 2t, and the second on a collisional-radiative calculation. Examples of compositions obtained with these two methods are presented. The hypotheses concerning the temperatures of populating of the internal energy levels are discussed in the light of these results. The third chapter of this thesis deals with the calculation of the thermodynamic properties at 2t of the plasma. The theoretical formulations of each of these properties are first recalled, and the results from these expressions are then presented and discussed, for the two methods of calculating the composition. The fourth chapter is dedicated to calculating the transport coefficients of a sf6-c2f4 plasma at 2t. This part is based on a bibliographic study of the already existing methods of calculation and the essential data to obtain these properties (collision integrals). For each property (viscosity, electrical conductivity and thermal conductivity) the various calculation methods identified in the literature are compared. The choice of the most appropriate calculation technique is made by comparing the results to the ETL. Particular attention is paid to the calculation of the reactive part of the thermal conductivity, and a formulation adapted to the needs of this work is proposed. The results from these expressions are presented and discussed following the same logic when in the previous chapter

Les simulations numériques sont devenues un outil indispensable dans la conception des chambres de coupure des disjoncteurs électriques haute tension. Elles sont utilisées non seulement dans le dimensionnement des différentes pièces, mais elles fournissent également une aide précieuse dans la compréhension des phénomènes intervenant entre les deux électrodes au moment de la coupure. L’arc électrique généré entre ces deux électrodes rassemble de nombreux domaines de la physique plus ou moins complexes. Tous ces phénomènes ne sont pas encore parfaitement compris. Avec l’évolution de la puissance de calcul, ces simulations peuvent prendre en compte de plus en plus de phénomènes. Mais pour des raisons de temps de développement, la question des phénomènes à prendre en compte dans ces simulations se pose. Le but de telles simulations est de déterminer de manière rapide si une configuration est plus ou moins capable qu’une autre de couper sous une contrainte donnée. Ainsi, il est important de prendre en compte uniquement les phénomènes physiques importants et nécessaires pour avoir une réponse la plus décisive possible et la plus rapide possible, de la réussite ou non à la coupure d’une configuration testée. Dans cette thèse, nous nous sommes particulièrement intéressés aux déséquilibres thermiques et chimiques qui pourraient intervenir dans les disjoncteurs électriques haute tension au moment de la coupure. En effet, pour des raisons de temps et de coût de calcul, la plupart des simulations numériques actuelles sont réalisées en faisant une hypothèse forte : l’hypothèse d’Equilibre Thermodynamique Local (ETL). Cette hypothèse consiste à considérer que dans chaque maille de notre domaine d’étude et à chaque pas de temps, on a un équilibre thermodynamique réalisé. Faire cette hypothèse nous permet d’utiliser les lois de conservation (masse, quantité de mouvement et énergie) en allégeant le problème. Mais en réalité, cette hypothèse est mise à mal dès que l’on est en présence de forts gradients de température ou de densité. Pour réaliser ces simulations, le code numérique CARBUR a été utilisé. Des modules d’arc électrique (effet Joule et rayonnement) et d’électrode mobile ont été implémentés afin de pouvoir simuler au mieux le comportement du gaz présent dans les disjoncteurs électriques haute tension. Six études différentes ont été réalisées et sont présentées. Ces études portent sur les influences de la forme du bout des électrodes, d’une modélisation en Navier-Stokes par rapport à une modélisation en Euler, de la nature du gaz (SF6, CO2 et N2), du déséquilibre thermique dans le cas de l’azote ou encore du positionnement des termes sources de l’arc électrique dans les différentes équations d’évolution des énergies. Dans ce travail, une étude sur différents modèles cinétiques chimiques est proposée. Dans ces modèles, 5 espèces chimiques sont présentes : N2, N, N+, N2+ et e-. En ce qui concerne la température, on en distingue 4 : T, TVib-N2, TVib-N2+ et Te
The numerical simulations are become a very important tool to design the high voltage circuit breaker (HVCB) chamber. They help for the understanding of the different phenomena which can take place between the 2 electrodes during an interruption process. The electric arc brings together many fields of physics more or less complex and many of these phenomena are still poorly studied. So many aspects remain to be explored to improve simulations. With the increase of the calculation power, these numerical simulations can take into account more phenomena. However, for reasonable simulation times, we need to know which phenomena are preponderant. The aim of these numerical simulations is to rapidly conclude on the capacity of geometry to success an interruption process compared to different other geometries, under a given stress. In this PhD dissertation, we are particularly interested on thermal and chemical non equilibrium that can occur in HVCB during an interruption process. Currently, most simulations are carried out with a strong hypothesis: the hypothesis of Local Thermodynamic Equilibrium (LTE). This assumption allows us to alleviate the problem and to reduce the computing time. But this assumption becomes not valid when high temperature or density gradients occur. To do these simulations, the CARBUR numerical code has been used. In order to simulate flow behaviors in HVCB, an electrical arc (Joule effect and radiation) model and a module of mobile electrode have been added. Six different studies have been done and are presented: influence of the electrode shape, influence of the Navier-Stokes equations compared to the Euler equations, influence of the gas (SF6, CO2 et N2), influence of the thermal non equilibrium in a nitrogen case, influence of the position of the arc source terms in the different energy equations. In this work, a study on different nitrogen chemical kinetics is proposed. In these models, 5 chemical species are distinguished: N2, N, N+, N2+ and e-. Finally, 4 different temperatures are used: T, TVib-N2, TVib-N2+ and Te

Cette thèse est consacrée à l’étude du transport réactif dans les réserves en eaux. Elle est structurée en deux parties distinctes : la première porte sur l’élaboration de solveurs chimiques et la seconde sur l’étude mathématique d’une classe de modèles décrivant des écoulements en eaux peu profondes en interaction avec les eaux de surface.Dans la première partie du travail, on s’intéresse à la résolution numérique des équilibres thermodynamiques qui conduisent à des systèmes non linéaires complexes et très mal conditionnés. Dans ce travail, on combine une formulation particulière du système d’équilibre chimique, appelée la méthode des fractions continues positives, avec deux méthodes numériques itératives, la méthode d’Accélération d’Anderson et des méthodes d’extrapolation vectorielle, à savoir les méthodes MPE (minimal polynomial extrapolation) et RRE (reduced rank extrapolation). Le principal avantage de ces approches est d’éviter de former la matrice jacobienne et donc d’éviter les problèmes liés aux mauvais conditionnements de la matrice. Des tests numériques sont faits, notamment sur le cas test de l’acide gallique et sur le cas test 1D de référence du benchmark MoMas. Ces essais illustrent la grande efficacité de cette approche par rapport aux résolutions classiques résultant de la méthode de Newton-Raphson. Dans la seconde partie de la thèse, on introduit et étudie des modèles de type Richards-Dupuit pour décrire les écoulements dans des aquifères peu profonds. L’idée est de coupler les deux types d’écoulements principaux présents dans l’aquifère : celui de la partie insaturée avec celui de la partie saturée. Le premier est décrit par le problème classique de Richards dans la frange capillaire supérieure.Le second résulte de l’approximation de Dupuit après intégration verticale des lois de conservation entre le fond de l’aquifère et l’interface de saturation. Le modèle final consiste en un système fortement couplé d’edp de type parabolique qui sont définies sur un domaine dépendant du temps. Nous montrons comment la prise en compte de la faible compressibilité du fluide permet d’éliminer la dégénérescence présente dans la dérivée temporelle de l’équation de Richards. Puis nous utilisons le cadre général des équations paraboliques dans des domaines non cylindriques introduit par Lions pour donner un résultat d’existence global en temps. Nous présentons l’analyse mathématique du premier modèle qui correspond au cas isotrope et non conservatif. Puis nous généralisons l’étude au cas anisotrope et conservatif
This thesis is devoted to the study of reactive transport in water reserves. It is structured in two distinct parts : the first deals with the development of chemical solvers and the second with the mathematical study of a class of models describing flows in shallow water interacting with the surface water. In the first part of the work, we focus on the numerical resolution of thermodynamic equilibria which lead to complex and very badly conditioned nonlinear systems. In this work, we combine aparticular formulation of the chemical equilibrium system, called the method of positive continuous fractions, with two iterative numerical methods, the Anderson Acceleration method and vector extrapolation methods, namely the MPE (minimal polynomial extrapolation) and RRE (reduced rank extrapolation) methods.The main advantage of these approaches is to avoid forming the Jacobian matrix and thus to avoid problems linked to bad conditioning of the matrix. Numerical tests are performed, especially on the test case of gallic acid and on the reference 1D case of the MoMas benchmark. These tests illustrate the great efficiency of this approach compared to classical solutions resulting from the Newton-Raphson method. In the second part of the thesis, we introduce and study Richards-Dupuit type models to describe flows in shallow aquifers. The idea is to couple the two main types of flows in the aquifer : that of the unsaturated part with that of the saturated part. The first is described by the classic Richardsproblem in the upper capillary fringe. The second results from Dupuit’s approximation after vertical integration of the conservation laws between the bottom of the aquifer and the saturation interface. The final model consists of a strongly coupled system of parabolic type pde which are defined on a time dependent domain. We show how taking into account the low compressibility of the fluid makes it possible to eliminate the degeneration in the time derivative term of the Richards equation.Then we use the general framework of parabolic equations in non-cylindrical domains introduced by Lions to give a global existence result in time. We present the mathematical analysis of the first model which corresponds to the isotropic and non-conservative case. Then we generalize the study to the anisotropic and conservative case

The purpose of this work is to demonstrate the usability of irreversible thermodynamics and kinetic theory in describing slow steady state evaporation and condensation, analyze the statistical rate theory (SRT) approach, and investigate the physical phenomena involved. Recently large interface temperature jumps have been observed during steady state evaporation and condensation experiments; the vapor interface temperature was greater than the liquid interface temperature for condensation and evaporation. To predict the temperature jump, the SRT mass flux was introduced as an alternative to the established approaches of irreversible thermodynamics and kinetic theory of gases. Simple one dimensional planar and spherical models were developed for slow evaporation and condensation based on the experiments. We considered pure liquid water evaporation and condensation to, and from its own vapor. Expressions for the mass and energy fluxes across the interface were found using irreversible thermodynamics, kinetic theory, and SRT. The SRT theory does not have an energy flux expression, as a substitute we use the irreversible thermodynamics energy flux in the SRT model. The equations were then solved to yield the mass and energy fluxes, and the liquid and vapor temperature profiles. We find the interface temperature jump is dependant on the energy flux expression. The irreversible thermodynamics energy flux closely predicts the measured temperature jump and direction. Kinetic theory models do not predict the jump, however with incorporation of a velocity dependant condensation coefficient, kinetic theory can predict the correct temperature jump direction, and vapor interface temperature. All the models predict mass fluxes that agree with the measured data. We suggest the temperature jump direction is established based on the direction of the vapor conductive energy flux, and not the direction of the mass flux (condensation or evaporation). We conclude that irreversible thermodynamics, kinetic theoiy, and SRT can all be used to model steady state evaporation and condensation.

博士
國立交通大學
環境工程系所
100
Interpretation of redox potential variations during biological processes using linear non-equilibrium thermodynamic model Student:Hong-Bang Cheng Advisor: Jih-Gaw Lin Institute of Environmental Engineering National Chiao Tung University ABSTRACT Various forms of Nernst equation have been dceveloped using simplified assumptions and/or modifications to depict the process of reversible and irreversible thermodynamic reactions in terms of the oxidation reduction potential (ORP). However, these assumptions are sometimes inappropriate in the quantification of ORP for non-equilibrium systems. A linear non-equilibrium thermodynamic model, called MIRROR model No. 1 (MIcrobial Related Reduction and Oxidation Reaction Model No. 1), is proposed in this research for interpreting ORP of biological processes. In the proposed model, ORP is related to affinities of catabolism and anabolism, and the energy expenditure of catabolism and anabolism is directly proportional to overpotential (η), straight coefficient of electrode (LEE), and degree of coupling between catabolism and ORP electrode. In addition, modeling the ORP of the biological nitrification and denitrification processes is addressed using MIRROR model No. 1. Laboratory data based on temperature, dissolved oxygen, COD, amonium, nitrite, nitrate, pH and ORP, were excerpted from literature and used for calibrating the model to determine the optimal values of various stoichiometric, kinetic, and phenomenological model parameters. The calibrated model was used to simulate the ORP variation of a biological nitrification and denitrifcation processes. The simulation results are in good correlation with the experimental observations (R2>0.93). Additionally, the performance of MIRROR model No.1 was compared with a commonly used modified-Nernst equation for simulating the biological nitrification and denitrification processes. MIRROR model No.1 has superior efficiency based on statistical analyses on deviance (i.e. root mean square error and mean absolute error), residual analyses and model discrimination. Overall, MIRROR model No. 1 appears to be an effective alternative to several modified-Nernst equations for simulating the ORP of biological processes. The limitations of MIRROR Model No. 1 have also been discussed for expanding the applicability of this model. When the final ORP value of biological denitrification processes is between -80 to -160 mV, the deviance of simulation results using the model is within a narrow range. If the final ORP is lower than -160 mV, the deviance increases sharply. The occurrence of some other non-nitrogen biological processes such as biological sulfate reduction may affect the ORP measurement so that the deviance increases sharply when the final ORP decreases. There is a close relationship between the affinities of catabolism and the system ORP of the biological denitrification process, but the ORP variation per unit affinity of catabolism is not a constant but proportional to the molarity of electrons transferred catabolically. The linear relationship between redox potential and reaction rate that has been derived based on MIRROR model No.1 in this research is verified by using the experimental results reported in the literature. This linear relationship enables evaluation of the biological denitrification rate based on the real-time monitoring of the system ORP. In addition, MIRROR model No. 1 predicts a distinctive curvilinear dependence of redox potential on the utilization of a selected substrate in microbial processes. With the substrate is excess, the system ORP is a logarithmic function of the substrate concentration. When the substrate in question becomes limited, the system ORP is observed to be linearly proportional to the substrate concentration. Keywords: Nernst equation, MIRROR model No. 1, redox potential, biologcial nitrification and biological denitrification.

The chemical compositions of the atmospheres of late-type stars, as inferred from stellar spectroscopic analyses, provide vital clues to unravelling the history of stars, galaxies, and the cosmos as a whole. However, the vast majority of stellar spectroscopic analyses make at least two assumptions that severely limit their accuracy: that stellar atmospheres are one-dimensional (1D) and hydrostatic; and that the material in the line-forming regions is in local thermodynamic equilibrium (LTE). Real atmospheres of late-type stars have convective envelopes that require a 3D time-evolving hydrodynamical treatment, and also real atmospheres are generally not in LTE. In this thesis I develop tools for 3D non-LTE radiative transfer calculations in late-type stars, and use them to address two outstanding problems that are pertinent to oxygen, which is one of the most important elements in astronomy. First is the so-called solar mod- elling problem, wherein inferences about the structure of the Sun based on helioseismology are in significant disagreement with those inferences based on the current best estimate of the solar chemical composition (as deduced from spectroscopy) and standard solar interior models. It has been strongly argued in the literature that a higher solar oxygen abundance is needed to resolve this problem. Second is the so-called oxygen problem in metal-poor stars, wherein different oxygen abundance diagnostics give different oxygen abundances in metal-poor Milky Way disk and halo stars. In particular, this has meant that the Galactic [O/Fe] versus [Fe/H] trend, a key tracer of chemical evolution, is poorly constrained in the metal-poor regime. I present new 3D non-LTE analyses of oxygen and silicon lines in the solar spectrum. The inferred solar oxygen and silicon abundances, 8.70 ± 0.03 dex and 7.51 ± 0.03 dex respectively, are consistent with the current canonical values to within errors, so maintaining the status quo on the solar modelling problem. I also present 3D non-LTE spectra for atomic oxygen lines across a grid of 3D hydrodynamic model atmospheres. Such a grid facilitates 3D non-LTE analyses of stars other than the Sun. With this grid I present analyses of the [O/Fe] versus [Fe/H] trend from Galactic disk and halo stars, and I demonstrate that with accurate stellar parameters and 3D non-LTE modelling, concordant results can be achieved between the two key atomic oxygen diagnostics: the [Oi]630nm line, and the O i 777 nm lines. Lastly, I present a 3D non-LTE analysis of Fe i and Fe ii lines in four metal- poor benchmark stars: HD84937, HD122563, HD140283, and G64-12. I demonstrate that the 3D non-LTE iron abundances are typically 0.1 dex higher than the corresponding 1D non-LTE iron abundances. 3D effects of this order need to be accounted for if the Galactic [O/Fe] versus [Fe/H] relationship is to be properly constrained.

The present Ph.D. thesis aims at discussing theoretical aspects and arguments concerning thermodynamic methods and applications to fission and fusion nuclear plants. All parts of the thesis are rooted in the ground of the scientific literature, and all outcomes and conclusions corroborate the conceptual building with no disprove of any foundations constituting the framework accepted and shared by the whole scientific community. Though, clarifications, extensions, generalizations and applications of concepts and definitions represent primary outcomes deemed by the author beneficial for a rational and systematic perspective of Physics and Thermodynamics in the research and applications to technological and industrial developments. This abstract attempt to summarize state-of-the-art and references, methods, achievements, original results, future perspectives and is followed by an index breaking down all sections to enable an overview on the way the thesis is organized. The mechanical aspect of the entropy-exergy relationship, together with the thermal aspect usually considered, represents the outset of the research and one of the central topics. This very aspect leads to a formulation of physical exergy and chemical exergy based on both useful work and useful heat, or useful work and useful mass, representing first outcomes based on the concept of available energy of a thermodynamic system interacting with a reservoir. By virtue of the entropy-exergy relationship, this approach suggests that a mechanical entropy contribution can be defined, in addition to the already used thermal entropy contribution, for work interaction due to pressure and volume variations. The mechanical entropy is related to energy transfer through work interaction, and it is complementary to the thermal entropy that accounts energy transfer by means of heat interaction. Then, the logical sequence to get mechanical exergy expression to evaluate useful work withdrawn from available energy is demonstrated. Based on mechanical exergy expression, the mechanical entropy set forth is deduced in a general form valid for any process. Finally, the formulation of physical exergy is proposed that summarizes the contribution of either heat or work interactions and related thermal exergy as well as mechanical exergy that both result as the outcome from the available energy of the composite of the system interacting with a reservoir. This formulation contains an additional term that takes into account the volume and, consequently, the pressure that allow to evaluate exergy with respect to the reservoir characterized by constant pressure other than constant temperature. The basis and related conclusions of this paper are not in contrast with principles and theoretical framework of thermodynamics and highlight a more extended approach to exergy definitions already reported in literature that remain the reference ground of present analysis. The literature reports that equality of temperature, equality of potential and equality of pressure between a system and a reservoir are necessary conditions for the stable equilibrium of the system-reservoir composite or, in the opposite and equivalent logical inference, that stable equilibrium is a sufficient condition for equality. A novelty of the present study is to prove that equality of temperature, potential and pressure is also a sufficient condition for stable equilibrium, in addition to necessity, implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality. A subsequent implication is that the proof of the sufficiency of equality (or the necessity of stable equilibrium) is attained by means of the generalization of the entropy property, derived from the generalization of exergy property, which is used to demonstrate that stable equilibrium is a logical consequence of equality of generalized potential. This proof is underpinned by the Second Law statement and the Maximum-Entropy Principle based on the generalized entropy which depends on temperature, potential and pressure of the reservoir. The conclusion, based on these two novel concepts, consists of the theorem of necessity and sufficiency of stable equilibrium for equality of generalized potentials within a composite constituted by a system and a reservoir. Among all statements of Second Law, the existence and uniqueness of stable equilibrium, for each given value of energy content and composition of constituents of any system, has been adopted to define thermodynamic entropy by means of the impossibility of Perpetual Motion Machine of the Second Kind (PMM2) which is a consequence of the Second Law. Equality of temperature, chemical potential and pressure in many-particle systems are proved to be necessary conditions for the stable equilibrium. The proofs assume the stable equilibrium and derive, through the Highest-Entropy Principle, equality of temperature, chemical potential and pressure as a consequence. In this regard, a first novelty of the present research is to demonstrate that equality is also a sufficient condition, in addition to necessity, for stable equilibrium implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality of temperature potential and pressure addressed to as generalized potential. The second novelty is that the proof of sufficiency of equality, or necessity of stable equilibrium, is achieved by means of a generalization of entropy property, derived from a generalized definition of exergy, both being state and additive properties accounting for heat, mass and work interactions of the system underpinning the definition of Highest-Generalized-Entropy Principle adopted in the proof. To complement the physical meaning and the reasons behind the need of a generalized definition of thermodynamic entropy, it is proposed a logical relation of its formulation on the base of Gibbs equation expressing the First Law. Moreover, a step forward is the extension of the canonical Equation of State in the perspective of thermal and chemical aspect of microscopic configurations of a system related to inter-particle kinetic energy and inter-particle potential energy determining macroscopic parameters. As a consequence, a generalized State Equation is formulated accounting for thermal, chemical and mechanical thermodynamic potentials characterizing any system in any state. As far as the Non-Equilibrium Thermodynamic is concerned, the present research aims at discussing the hierarchical structure of so-called mesoscopic systems configuration. In this regard, thermodynamic and informational aspects of entropy concept are highlighted to propose a unitary perspective of its definitions as an inherent property of any system in any state, both physical and informational. The dualism and the relation between physical nature of information and the informational content of physical states of matter and phenomena play a fundamental role in the description of multi-scale systems characterized by hierarchical configurations. A method is proposed to generalize thermodynamic and informational entropy property and characterize the hierarchical structure of its canonical definition at macroscopic and microscopic levels of a system described in the domain of classical and quantum physics. The conceptual schema is based on dualisms and symmetries inherent to the geometric and kinematic configurations and interactions occurring in many-particle and few-particle thermodynamic systems. The hierarchical configuration of particles and sub-particles, representing the constitutive elements of physical systems, breaks down into levels characterized by particle masses subdivision, implying positions and velocities degrees of freedom multiplication. This hierarchy accommodates the allocation of phenomena and processes from higher to lower levels in the respect of the equipartition theorem of energy. However, the opposite and reversible process, from lower to higher level, is impossible by virtue of the Second Law, expressed as impossibility of Perpetual Motion Machine of the Second Kind (PMM2) remaining valid at all hierarchical levels, and the non-existence of Maxwell’s demon. Based on the generalized definition of entropy property, the hierarchical structure of entropy contribution and production balance, determined by degrees of freedom and constraints of systems configuration, is established. Moreover, as a consequence of the Second Law, the non-equipartition theorem of entropy is enunciated, which would be complementary to the equipartition theorem of energy derived from the First Law. A section is specifically dedicated to specialize Second Law analyses to characterize balances of properties, and efficiencies of processes, occurring in elemental fission and fusion nuclear reactions. The conceptual schema is underpinned by the paradigm of microscopic few-particle systems and the inter-particle kinetic energy and binding potential energy determined by interactions among atomic nuclei and subatomic particles in non-equilibrium states along irreversible phenomena. The definition here proposed for thermodynamic entropy calculation is based on energy and exergy both being measurable properties by means of those values calculated from particles mass defect and used to directly derive entropy balances along nuclear processes occurring in operating industrial plants. Finally, it is proposed a preliminary exergy analysis of EU DEMO pulsed fusion power plant considering the Primary Heat Transfer Systems, the Intermediate Heat Transfer System (IHTS) including the Energy Storage System (ESS) as a first option to ensure the continuity of electric power released to the grid. A second option here considered is a methane fired auxiliary boiler replacing the ESS. The Power Conversion System (PCS) performance is evaluated as well in the overall balance. The performance analysis is based on the exergy method to correctly assess the amount of exergy destruction determined by irreversible phenomena along the whole cyclic process. The pulse and dwell phases of the reactor operation are evaluated considering the state of the art of the ESS adopting molten salts alternate heating and storage in a hot tank followed by a cooling and recovery of molten salt in a cold tank to ensure the continuity of power release to the electrical grid. An alternative plant configuration is evaluated on the basis of an auxiliary boiler replacing the ESS with a 10% of the power produced by the reactor during pulse mode. The conclusive summary of main achievements and original outcomes is followed by proposals of future developments in different fields of theoretical and applied research and technology. These themes represent an outlook on the opportunities and initiatives originating from the passionate dedication effort spent along the here ended Doctorate.

In this work, we study the entropy production of relativistic quantum fluids at local thermodynamic equilibrium. In particular, we put forward a general method to calculate the entropy current in the framework of relativistic quantum statistical mechanics. We then apply our method to the study of two different systems, both of phenomenological concern in the context of heavy-ion collisions. The first system is a relativistic quantum fluid at global thermodynamic equilibrium with acceleration, whereas the second one is a relativistic quantum fluid with boost invariance. We calculate the thermal expectation value of the energy-momentum tensor, discuss renormalisation and work out the entropy current.