Relevant bibliographies by topics / Non-equilibrium and irreversible thermodynamic

Academic literature on the topic 'Non-equilibrium and irreversible thermodynamic'

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Published: 14 March 2023

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Journal articles on the topic "Non-equilibrium and irreversible thermodynamic"

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Pekař, Miloslav. "Thermodynamics and foundations of mass-action kinetics." Progress in Reaction Kinetics and Mechanism 30, no. 1-2 (June 2005): 3–113. http://dx.doi.org/10.3184/007967405777874868.

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A critical overview is given of phenomenological thermodynamic approaches to reaction rate equations of the type based on the law of mass-action. The review covers treatments based on classical equilibrium and irreversible (linear) thermodynamics, extended irreversible, rational and continuum thermodynamics. Special attention is devoted to affinity, the applications of activities in chemical kinetics and the importance of chemical potential. The review shows that chemical kinetics survives as the touchstone of these various thermody-namic theories. The traditional mass-action law is neither demonstrated nor proved and very often is only introduced post hoc into the framework of a particular thermodynamic theory, except for the case of rational thermodynamics. Most published “thermodynamic'’ kinetic equations are too complicated to find application in practical kinetics and have merely theoretical value. Solely rational thermodynamics can provide, in the specific case of a fluid reacting mixture, tractable rate equations which directly propose a possible reaction mechanism consistent with mass conservation and thermodynamics. It further shows that affinity alone cannot determine the reaction rate and should be supplemented by a quantity provisionally called constitutive affinity. Future research should focus on reaction rates in non-isotropic or non-homogeneous mixtures, the applicability of traditional (equilibrium) expressions relating chemical potential to activity in non-equilibrium states, and on using activities and activity coefficients determined under equilibrium in non-equilibrium states.
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Michaelian, Karo. "Non-Equilibrium Thermodynamic Foundations of the Origin of Life." Foundations 2, no. 1 (March 21, 2022): 308–37. http://dx.doi.org/10.3390/foundations2010022.

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There is little doubt that life’s origin followed from the known physical and chemical laws of Nature. The most general scientific framework incorporating the laws of Nature and applicable to most known processes to good approximation, is that of thermodynamics and its extensions to treat out-of-equilibrium phenomena. The event of the origin of life should therefore also be amenable to such an analysis. In this review paper, I describe the non-equilibrium thermodynamic foundations of the origin of life for the non-expert from the perspective of the “Thermodynamic Dissipation Theory for the Origin of Life” which is founded on Classical Irreversible Thermodynamic theory developed by Lars Onsager, Ilya Prigogine, and coworkers. A Glossary of Thermodynamic Terms can be found at the end of the article to aid the reader.
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Tangde, Vijay M., and Anil A. Bhalekar. "How Flexible Is the Concept of Local Thermodynamic Equilibrium?" Entropy 25, no. 1 (January 10, 2023): 145. http://dx.doi.org/10.3390/e25010145.

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It has been demonstrated by using generalized phenomenological irreversible thermodynamic theory (GPITT) that by replacing the conventional composition variables {xk} by the quantum level composition variables {x˜k,j} corresponding to the nonequilibrium population of the quantum states, the resultant description remains well within the local thermodynamic equilibrium (LTE) domain. The next attempt is to replace the quantum level composition variables by their respective macroscopic manifestations as variables. For example, these manifestations are, say, the observance of fluorescence and phosphorescence, existence of physical fluxes, and ability to register various spectra (microwave, IR, UV-VIS, ESR, NMR, etc.). This exercise results in a framework that resembles with the thermodynamics with internal variables (TIV), which too is obtained as a framework within the LTE domain. This TIV-type framework is easily transformed to an extended irreversible thermodynamics (EIT) type framework, which uses physical fluxes as additional variables. The GPITT in EIT version is also obtained well within the LTE domain. Thus, GPITT becomes a complete version of classical irreversible thermodynamics (CIT). It is demonstrated that LTE is much more flexible than what CIT impresses upon. This conclusion is based on the realization that the spatial uniformity for each tiny pocket (cell) of a spatially non-uniform system remains intact while developing GPITT and obviously in its other versions.
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Bryant, Samuel J., and Benjamin B. Machta. "Energy dissipation bounds for autonomous thermodynamic cycles." Proceedings of the National Academy of Sciences 117, no. 7 (February 4, 2020): 3478–83. http://dx.doi.org/10.1073/pnas.1915676117.

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How much free energy is irreversibly lost during a thermodynamic process? For deterministic protocols, lower bounds on energy dissipation arise from the thermodynamic friction associated with pushing a system out of equilibrium in finite time. Recent work has also bounded the cost of precisely moving a single degree of freedom. Using stochastic thermodynamics, we compute the total energy cost of an autonomously controlled system by considering both thermodynamic friction and the entropic cost of precisely directing a single control parameter. Our result suggests a challenge to the usual understanding of the adiabatic limit: Here, even infinitely slow protocols are energetically irreversible.
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Abourabia, A. M., and T. Z. Abdel Wahid. "The unsteady Boltzmann kinetic equation and non-equilibrium thermodynamics of an electron gas for the Rayleigh flow problem." Canadian Journal of Physics 88, no. 7 (July 2010): 501–11. http://dx.doi.org/10.1139/p10-032.

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In the framework of irreversible thermodynamics, the characteristics of the Rayleigh flow problem of a rarified electron gas extracted from neutral atoms is examined and proved to obey the entropic behavior for gas systems. A model kinetic equation of the BGK (Bhatnager–Gross–Krook) type is solved, using the method of moments with a two-sided distribution function. Various macroscopic properties of the electron gas, such as the mean velocity, the shear stress, and the viscosity coefficient, together with the induced electric and magnetic fields, are investigated with respect to both distance and time. The distinction between the perturbed velocity distribution functions and the equilibrium velocity distribution function at different time values is illustrated. We restrict our study to the domain of irreversible thermodynamics processes with small deviation from the equilibrium state to estimate the entropy, entropy production, entropy flux, thermodynamic force, and kinetic coefficient and verify the celebrated Boltzmann H-theorem for non-equilibrium thermodynamic properties of the system. The ratios between the different contributions of the internal energy changes, based upon the total derivatives of the extensive parameters, are predicted via Gibbs’ equation for both diamagnetic and paramagnetic plasmas. The results are applied to a typical model of laboratory argon plasma.
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Ganghoffer, Jean-François, and Rachid Rahouadj. "Thermodynamic formulations of continuum growth of solid bodies." Mathematics and Mechanics of Solids 22, no. 5 (December 10, 2015): 1027–46. http://dx.doi.org/10.1177/1081286515616228.

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The thermodynamics of open systems exchanging mass, heat, energy, and entropy with their environment is examined as a convenient unifying framework to describe the evolution of growing solid bodies in the context of volumetric growth. Following the theory of non-equilibrium thermodynamics (NET) introduced by De Donder and followers from the Brussels School of Thermodynamics, the formulation of the NET of irreversible processes for multicomponent solid bodies is shortly reviewed. In the second part, extending the framework of NET to open thermodynamic systems, the balance laws for continuum solid bodies undergoing growth phenomena incorporating mass sources and mass fluxes are expressed, leading to a formulation of the second principle highlighting the duality between irreversible fluxes and conjugated driving forces. A connection between NET and the open system thermodynamic formulation for growing continuum solid bodies is obtained by interpreting the balance laws with source terms as contributions from an external reservoir of nutrients.
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Öttinger, Hans Christian. "GENERIC Integrators: Structure Preserving Time Integration for Thermodynamic Systems." Journal of Non-Equilibrium Thermodynamics 43, no. 2 (April 25, 2018): 89–100. http://dx.doi.org/10.1515/jnet-2017-0034.

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AbstractThermodynamically admissible evolution equations for non-equilibrium systems are known to possess a distinct mathematical structure. Within the GENERIC (general equation for the non-equilibrium reversible–irreversible coupling) framework of non-equilibrium thermodynamics, which is based on continuous time evolution, we investigate the possibility of preserving all the structural elements in time-discretized equations. Our approach, which follows Moser’s [1] construction of symplectic integrators for Hamiltonian systems, is illustrated for the damped harmonic oscillator. Alternative approaches are sketched.
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Dewey, T. Gregory. "Algorithmic Complexity and Thermodynamics of Fractal Growth Processes." Fractals 05, no. 04 (December 1997): 697–706. http://dx.doi.org/10.1142/s0218348x97000565.

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A statistical mechanical formalism is developed using the computer information concepts of algorithmic complexity and Kolmogorov universal probability. This formalism provides a thermodynamic description of microstates of a system. For an isolated classical system, the algorithmic complexity is equal to the thermodynamic entropy. This approach does not rely on probabilistic ensemble concepts and can be applied to non-ergodic systems. An H-function is developed from the Kolmogorov universal probability that satisfies the properties of an entropy function. Using this approach, the thermodynamics of irreversible growth processes far from equilibrium can be investigated. Entropy functions for fractal growth processes far from equilibrium are developed from the algorithmic complexity and are seen to be similar to Flory-type equilibrium functions. This development does not require energy minimization procedures associated with equilibrium arguments. Using this approach, constraints can be put on the types of mean field models that will yield fractal structures. The algorithmic complexity of a system can also be used to explore the role of fluctuations and criticality in highly ordered systems.
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GAO, TIANFU, and JINCAN CHEN. "NON-EQUILIBRIUM THERMODYNAMIC ANALYSIS ON THE PERFORMANCE OF AN IRREVERSIBLE THERMALLY DRIVEN BROWNIAN MOTOR." Modern Physics Letters B 24, no. 03 (January 30, 2010): 325–33. http://dx.doi.org/10.1142/s0217984910022408.

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Based on the general model of thermally-driven Brownian motors, an equivalent cycle system is established and the Onsager coefficients and efficiency at the maximum power output of the system are analytically calculated from non-equilibrium thermodynamics. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are affected by the main irreversibilities existing in practical systems. Only when the heat leak and the kinetic energy change of the particle in the system are negligible, can the determinant of the Onsager matrix vanish. It is also found that in the frame of non-equilibrium thermodynamics, the power output and efficiency of an irreversible Brownian motor can be expressed to be the same form as those of an irreversible Carnot heat engine, so the results obtained here are of general significance. Moreover, these results are used to analyze the performance characteristics of a class of thermally-driven Brownian motors so that some important conclusions in literature may be directly derived from the present paper.
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Mendoza, D. F., and S. Kjelstrup. "Modeling a non-equilibrium distillation stage using irreversible thermodynamics." Chemical Engineering Science 66, no. 12 (June 2011): 2713–22. http://dx.doi.org/10.1016/j.ces.2011.03.023.

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

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Ramirez, Estay Hector. "Control of irreversible thermodynamic processes using port-Hamiltonian systems defined on pseudo-Poisson and contact structures." Thesis, Lyon 1, 2012. http://www.theses.fr/2012LYO10033/document.

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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
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GRISOLIA, GIULIA. "Biofuels from micro-organisms: Thermodynamic analysis of sustainability." Doctoral thesis, Politecnico di Torino, 2022. https://hdl.handle.net/11583/2973986.

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Packwood, Daniel Miles. "Theoretical and Experimental Studies of the Gas-Liquid Interface." Thesis, University of Canterbury. Department of Chemistry, 2010. http://hdl.handle.net/10092/4618.

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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.
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Liu, Ensheng Yuan Jian-Min. "Sensitivity, non-equilibrium thermodynamic and control analyses of insulin metabolic signaling pathways /." Philadelphia, Pa. : Drexel University, 2007. http://hdl.handle.net/1860/1862.

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Mariani, Riccardo. "Irreversible parallel dynamics in statistical mechanics." Thesis, Aix-Marseille, 2018. http://www.theses.fr/2018AIXM0744/document.

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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 $\varepsilon = 0$
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Holladay, Robert Tyler. "Steepest-Entropy-Ascent Quantum Thermodynamic Modeling of Quantum Information and Quantum Computing Systems." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/94630.

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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.
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Schubert, Sven. "Stochastic and temperature-related aspects of the Preisach model of hysteresis." Doctoral thesis, Universitätsbibliothek Chemnitz, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-70798.

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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
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Li, Guanchen. "Non-equilibrium Thermodynamic Approach Based on the Steepest-Entropy-Ascent Framework Applicable across All Temporal and Spatial Scales." Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/78354.

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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.
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Davie, Stuart James. "Relative Free Energies from Non-Equilibrium Simulations: Application to Changes in Density." Thesis, Griffith University, 2014. http://hdl.handle.net/10072/365922.

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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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LEGGIO, Bruno. "Quantum fluctuations and correlations in equilibrium and nonequilibrium thermodynamics." Doctoral thesis, Università degli Studi di Palermo, 2014. http://hdl.handle.net/10447/90914.

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Books on the topic "Non-equilibrium and irreversible thermodynamic"

1

Haslach, Henry W. Maximum dissipation non-equilibrium thermodynamics and its geometric structure. New York: Springer, 2010.

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Woods, L. C. The thermodynamics of fluid systems. Oxford [Oxfordshire]: Clarendon Press, 1985.

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Nagnibeda, Ekaterina A. Transport properties of NO in nonequilibrium flows. Noordwijk, The Netherlands: ESA Publications Division, 2005.

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Energy and entropy: Equilibrium to stationary states. New York: Springer, 2010.

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Alternative mathematical theory of non-equilibrium phenomena. Boston, Mass: Academic Press, 1997.

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Moreno-Piraján, Juan Carlos. Thermodynamics: Systems in equilibrium and non-equilibrium. Croatia: InTech, 2011.

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Casassus, Jaime. Equilibrium commodity prices with irreversible investment and non-linear technology. Cambridge, Mass: National Bureau of Economic Research, 2005.

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Rastogi, R. P. Introduction to non-equilibrium physical chemistry: Towards complexity and non-linear science. Amsterdam: Elsevier, 2007.

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Greenberg, Jacob H. Thermodynamic Basis of Crystal Growth: P-T-X Phase Equilibrium and Non-Stoichiometry. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002.

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Savolainen, Pekka. Modeling of non-isothermal vapor membrane separation with thermodynamic models and generalized mass transfer equations. Lappeenranta, Finland: Lappeenranta University of Technology, 2002.

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Book chapters on the topic "Non-equilibrium and irreversible thermodynamic"

1

Jou, David, José Casas-Vázquez, and Georgy Lebon. "Non-equilibrium Statistical Mechanics." In Extended Irreversible Thermodynamics, 113–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-97430-4_5.

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Jou, David, José Casas-Vázquez, and Georgy Lebon. "Non-equilibrium Statistical Mechanics." In Extended Irreversible Thermodynamics, 131–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-97671-1_5.

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Jou, David, José Casas-Vázquez, and Georgy Lebon. "Classical and Rational Formulations of Non-equilibrium Thermodynamics." In Extended Irreversible Thermodynamics, 3–39. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-97430-4_1.

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Jou, David, José Casas-Vázquez, and Georgy Lebon. "Classical and Rational Formulations of Non-equilibrium Thermodynamics." In Extended Irreversible Thermodynamics, 3–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-97671-1_1.

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Jou, David, José Casas-Vázquez, and Georgy Lebon. "Extended Irreversible Thermodynamics: Non-equilibrium Equations of State." In Extended Irreversible Thermodynamics, 71–89. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-3074-0_3.

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Jou, David, José Casas-Vázquez, and Georgy Lebon. "Classical and Rational Formulations of Non-equilibrium Thermodynamics." In Extended Irreversible Thermodynamics, 3–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56565-6_1.

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Jou, David, José Casas-Vázquez, and Georgy Lebon. "Extended Irreversible Thermodynamics: Non-equilibrium Equations of State." In Extended Irreversible Thermodynamics, 73–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56565-6_3.

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Jou, David, José Casas-Vázquez, and Georgy Lebon. "Classical, Rational and Hamiltonian Formulations of Non-equilibrium Thermodynamics." In Extended Irreversible Thermodynamics, 3–40. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-3074-0_1.

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Zhang, Zhihong, Wenlong Qin, Jiapei Zhang, Zhaogang Xu, and Fei Guo. "A Non-equilibrium Adsorption Model Based on Irreversible Thermodynamics." In Environmental Science and Engineering, 521–27. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-2221-1_56.

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Hütter, Markus, and Bob Svendsen. "On the Formulation of Continuum Thermodynamic Models for Solids as General Equations for Non-equilibrium Reversible-Irreversible Coupling." In Methods and Tastes in Modern Continuum Mechanics, 357–68. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-94-007-1884-5_23.

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Conference papers on the topic "Non-equilibrium and irreversible thermodynamic"

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Dai, Zhendong. "An Irreversible Thermodynamic Theory of Friction and Wear." In ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2008. http://dx.doi.org/10.1115/esda2008-59024.

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Friction and wear are typical irreversible processes. Friction irreversibly degrades and dissipates high quality energy and wear irreversibly removes materials from the load-carrying surface. The two irreversible processes can be presented by entropy production, which is a non-negative quantity based on irreversible thermodynamics and thus serves as a basis for the systematic description of irreversible processes occurring in tribological system. In this paper, a thermodynamic framework has been presented for the mechanisms of friction and wear of continuum materials, where entropy production is used as the sole measure of energy dissipation and material damage evolution in the system. As a result, there is no need for physically meaningless empirical parameters to define the phenomenological frictional and wear parameters to trace tribological evolution in a friction and wear system. To validate the model, predictions are compared with experimental results, which indicate that entropy production can be used as a friction and wear evolution metric. The theory is founded on the basic premise that a solid continuum obeys the first and second laws of thermodynamics.
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Smith, Charles E., and Michael R. von Spakovsky. "Time Evoultion of Entropy in a System Comprised of a Boltzmann Type Gas: An Application of the Beretta Equation of Motion." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-42933.

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Basing his work on a new formulation of thermodynamics called the Unified Quantum Theory of Mechanics and Thermodynamics first published in a series of four ground breaking papers in 1976 (Hatsopoulos and Gyftopoulos, 1976a, b, c, d), Beretta develops a dynamical postulate (Beretta et al. 1984; Beretta, Gyftopoulos, and Park, 1985) consistent both with the non-dynamical quantum mechanical postulates of the Unified Theory as well as with its thermodynamic ones (the 2nd Law in particular). The theory itself simply and elegantly extends in a unified fashion the concepts of thermodynamics to quantum mechanics and the concepts of quantum mechanics to thermodynamics. It does so without the bridge traditionally used, i.e. statistical mechanics, eliminating a number of the ambiguities, tautologies, and inconsistencies (including a built-in violation of the 2nd Law) inherent in the presentations of both Classical and Statistical Thermodynamics. This new formulation generalizes thermodynamics so that it applies to all systems large or small (including one particle systems) either in a state of thermodynamic (i.e. stable) equilibrium or not in a state of thermodynamic equilibrium. The Beretta equation of motion describes the time evolution of the state of a system via a density operator which is uniquely based on an unambiguous preparation of an ensemble of identical systems, i.e. the so-called homogenous or irreducible ensemble, and does so both for unitary and non-unitary reversible as well as irreversible processes. In this paper, we present a simple application of this general equation of motion to the time evolution of the entropy of a closed system comprised of a Boltzmann type gas consisting of one or of many particles undergoing an irreversible process. A number of different energy eigenlevels and initial states and their effects on entropy generation and the final state of maximum entropy, i.e. stable equilibrium, are examined. A simple time-dependent work interaction is introduced into the formulation to show how this in turn affects the evolution of the state of the system.
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Imanian, Anahita, and Mohammad Modarres. "Corrosion-Fatigue Structural Integrity Assessment Using a Thermodynamic Entropy Based Damage Approach." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-53452.

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Using fundamentals of irreversible thermodynamics, with specific focus on entropy generation, this paper studies the structural integrity of degraded materials. All damage mechanisms share a common feature namely energy dissipation. Dissipation, as a fundamental measure for irreversibility in a thermodynamic treatment of non-equilibrium processes, is quantified by entropy generation. Based on the theoretical relationship between entropy generation and generalized thermodynamic forces and fluxes, the entropic damage is measured during a corrosion-fatigue degradation experiment. Life estimation of components, which were subject to complex corrosion-fatigue degradation mechanism, was then estimated through a proposed entropic-based prognostic framework. The performance of predictions was evaluated and compared with previous predictions in terms of the influence of additional features on components health assessment.
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von Spakovsky, Michael R., Charles E. Smith, and Vittorio Verda. "Quantum Thermodynamics for the Modeling of Hydrogen Storage on a Carbon Nanotube." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-67424.

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A typical approach for modeling systems at a nanoscale in states of non-equilibrium undergoing an irreversible process is to use an ad hoc mixture of molecular dynamics (linear and nonlinear), i.e. classical mechanics, coupled to assumptions of stable equilibrium which allow one via analogy to incorporate equilibrium thermodynamic state information such as temperature and pressure into the modeling process. However, such an approach cannot describe the actual thermodynamic evolution in state which occurs in these systems since the equation of motion used (Newton’s second law) can only describe the evolution in state from one mechanical state to another. To capture the actual thermodynamic evolution, a more general equation of motion is needed. Such an equation has been proposed, i.e. the Beretta equation of motion, as part of a general theory, which unifies (not simply bridges as is the case in statistical thermodynamics) quantum mechanics and thermodynamics. It is called the unified quantum theory of mechanics and thermodynamics or quantum thermodynamics. This equation, which strictly satisfies all of the implications of the laws of thermodynamics, including the second law, as well as of quantum mechanics, describes the thermodynamic evolution in state of a system in non-equilibrium regardless of whether or not the system is in a state far from or close to stable equilibrium. This theory and its dynamical postulate are used here to model the storage of hydrogen in an isolated box modeled in 1D and 2D with a carbon atom at one end of the box in 1D and a carbon nanotube in the middle of the box in 2D. The system is prepared in a state with the hydrogen molecules initially far from stable equilibrium, after which the system is allowed to relax (evolve) to a state of stable equilibrium. The so-called energy eigenvalue problem is used to determine the energy eigenlevels and eigenstates of the system, while the nonlinear Beretta equation of motion is used to determine the evolution of the thermodynamic state of the system as well as the spatial distributions of the hydrogen molecules in time. The results of our initial simulations show in detail the trajectory of the state of the system as the hydrogen molecules, which are initially arranged to be far from the carbon atom or the carbon nanotube, are seen to spread out in the container and eventually become more concentrated near the carbon atom or atoms.
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Trancossi, Michele, and Pascoa Jose. "Irreversibility Analysis, Design, and Optimization of a Combined Hybrid Hot Air and Buoyant Gas Balloon for Stratospheric Persistence." In ASME 2021 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/imece2021-69681.

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Abstract This paper presents the heat and mass transfer model and the design analysis of ALCHEMIST (Atmospheric Laboratory for the study of Circulation at High-altitude, Exchange of Markers and Intercontinental routes between Stratosphere and Troposphere). It is an innovative hybrid balloon project. It is constituted by coupling an external unconventional parachute envelope and a Hydrogen balloon. The dynamic equilibrium conditions with the surrounding atmosphere are considered. The system has been modeled as a limited unsteady irreversible thermodynamic living system. The mission is considered as an evolution of the system in equilibrium with the surrounding environment. Hence, a thermodynamic model based on irreversible thermodynamics is presented. The results according to both first and second law are produced and compared to actual flight data. The primary physical processes responsible for balloon performance aloft are accurately modeled in the proposed optimization process. The results demonstrate that the system could be optimized up to a stratospheric altitude around 30 km and shows that second law optimization produces an effective performance improvement.
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Chavez, Rosa-Hilda, Jazmin Cortez-Gonzalez, Javier de J. Guadarrama, and Abel Hernandez-Guerrero. "Thermodynamic Analysis of the CO2 Gas Removal Process." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43002.

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The present paper describes the thermodynamic analysis of the carbon dioxide (CO2) gas removal process in two separated columns with absorption/stripping sections respectively. This process is characterized as mass transfer enhanced by chemical reaction, in which the presence of an alkanolamine enhances the solubility of an acid gas in the aqueous phase at a constant value of the equilibrium partial pressure. A very useful procedure for analyzing a process is by means of the Second Law of Thermodynamics. Thermodynamic analyses based on the concepts of irreversible entropy increase have frequently been suggested as pointers to sources of inefficiency in chemical processes. Furthermore, they point out where the irreversibilities of the process are located, and provide a generalized discussion from the successful application of the technique.
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Basaran, Cemal, and Shihua Nie. "Irreversible Thermodynamics for Damage Mechanics of Solid Materials." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32937.

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In this paper a thermodynamic framework has been presented for damage mechanics of solids materials. Traditional damage mechanics theory uses damage potential function to trace damage evolution. In this framework entropy production is used as a measure of damage in the system. As a result there is no need for physically meaningless empirical material parameters to define a damage potential function. It is assumed that entropy production is non-negative for solids.
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Guo, Jiangfeng, Mingtian Xu, and Lin Cheng. "A New Criterion for Assessing Heat Exchanger Performance." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-22315.

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The principle of minimum entropy production has played an important role in the development of non-equilibrium thermodynamics. Inspired by this principle, Bejan derived the expression of the local entropy production rate for heat convection and established the entropy production minimization approach for the heat exchanger optimization design. Although one can obtain the entropy production distribution in the heat exchanger numerically, it can not directly been employed to examine the heat exchanger performance. Tondeur and Kvaalen found that the entropy production uniformity is closely related to the heat exchanger performance. In the present work, based on Tondear and Kvaalen’s work, an entropy production uniformity factor is defined, which quantifies the uniformity of the local entropy generation distribution in heat exchanger. Numerical results of the heat transfer in a rectangular channel show that the larger entropy production uniformity factor implies less irreversible loses. Therefore, this factor can serve as a thermodynamic figure of merit for assessing the heat exchanger performance.
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Rieder, William G., and Lyle D. Prunty. "An Alternative Modeling Procedure for Describing Coupled Heat and Mass Transfer in Semi-Dry Porous Media Samples." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-0797.

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Abstract An alternative modeling approach is described for unsaturated porous-media samples, where both irreversible and equilibrium thermodynamic arguments are used to set up a simple coupled differential equation set. Predictions based on numerical evaluations of the foregoing set demonstrate the nonlinear temperature and fluid profiles that have been observed in experiments with unsaturated water-in-soil samples. Minimal literature and empirical input is required to quantify parameters. Comparisons with data from small scale experiments show good agreements. It is argued that such an approach could lead to acceptable simulation schemes for poorly-defined media containing several nonreacting fluids.
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Fito, Pedro J., Juan Angel Tomas-Egea, and Marta Castro-Giraldez. "Thermodynamic model of freeze-drying of poultry breast using infrared thermography." In 21st International Drying Symposium. Valencia: Universitat Politècnica València, 2018. http://dx.doi.org/10.4995/ids2018.2018.7756.

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Food dehydration is one of a main process to preserve meal. In order to optimaze a freeze-drying operation a physic model is needed to well describe the thermodynamic behaviors involved in this process. In this work, a thermographic camera and different physico-chemical determinations are used to monitor many phenomena that occur during the lyophilization of poultry breast. Finally, a non-continuous irreversible thermodynamic model, based on thermal infrared measures and in shrinkage/swelling mechanism, has been developed, wich explains the behaviours produced throughout the meat freeze-drying process. Keywords: freeze-drying, thermodynamic model, infrared thermography, poultry.
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Reports on the topic "Non-equilibrium and irreversible thermodynamic"

1

Casassus, Jaime, Pierre Collin-Dufresne, and Bryan Routledge. Equilibrium Commodity Prices with Irreversible Investment and Non-Linear Technology. Cambridge, MA: National Bureau of Economic Research, December 2005. http://dx.doi.org/10.3386/w11864.

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Zerkle, D., and H. Krier. Non-Local Thermodynamic Equilibrium in Laser Sustained Plasmas. Fort Belvoir, VA: Defense Technical Information Center, June 1992. http://dx.doi.org/10.21236/ada253389.

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McCartney, L. N., and E. J. Dickinson. Development of consistent local thermodynamic relations for non-equilibrium multi-component fluid systems. National Physical Laboratory, June 2021. http://dx.doi.org/10.47120/npl.mat98.

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Mertens, Christopher J., Martin G. Mlynczak, Manuel Lopez-Puertas, Peter P. Wintersteiner, Richard H. Picard, Jeremy R. Winick, Larry L. Gordley, James M. Russell, and III. Retrieval of Kinetic Temperature and Carbon Dioxide Abundance From Non-Local Thermodynamic Equilibrium Limb Emission Measurements Made by the SABER Experiment on the TIMED Satellite. Fort Belvoir, VA: Defense Technical Information Center, January 2003. http://dx.doi.org/10.21236/ada439211.

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Crowley, David, Yitzhak Hadar, and Yona Chen. Rhizosphere Ecology of Plant-Beneficial Microorganisms. United States Department of Agriculture, February 2000. http://dx.doi.org/10.32747/2000.7695843.bard.

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Rhizoferrin, a siderophore produced by Rhizopus arrhizus, has been shown in previous studies to be an outstanding Fe carrier to plants. However, calculations based on stability constants and thermodynamic equilibrium lead to contradicting conclusions. In this study a kinetic approach was employed to elucidate this apparent contradiction and to determine the behavior of rhizoferrin under conditions representing soil and nutrient solutions. Stability of Fe3+ complexes in nutrient solution, rate of metal exchange with Ca, and rate of Fe extraction by the free ligand were monitored for rhizoferrin and other chelating agents by 55Fe labeling. Ferric complexes of rhizoferrin, desferri-ferrioxamine-B (DFOB), and ethylenediamine-di(o-hydroxyphenylacetic acid) (EDDHA) were found to be stable in nutrient solution at pH 7.5 for 31 days, while ferric complexes of ethylenediaminetetraacetic acid (EDTA) and mugineic acid (MA) lost 50% of the chelated Fe within 2 days. Fe-Ca exchange in Ca solutions at pH 8.7 revealed rhizoferrin to hold Fe at non-equilibrium state for 3-4 weeks at 3.3 mM Ca and for longer periods at lower Ca concentrations. EDTA lost the ferric ion at a faster rate under the same conditions. Fe extraction from freshly prepared Fe-hydroxide at pH 8.7 and with 3.2 mM Ca was slow and followed the order. DFOB > EDDHA > MA > rhizoferrin > EDTA. Based on these results we suggest that a kinetic rather than equilibrium approach should be the basis for predictions of Fe-chelates efficiency. We conclude that the non-equilibrium state of rhizoferrin is of crucial importance for its behavior as a Fe carrier to plants.
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