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Journal articles on the topic 'Thermodynamics'
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1
Li, Li-Fang, and Jian-Yang Zhu. "Thermodynamics in Loop Quantum Cosmology." Advances in High Energy Physics 2009 (2009): 1–9. http://dx.doi.org/10.1155/2009/905705.
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Loop quantum cosmology (LQC) is very powerful to deal with the behavior of early universe. Moreover, the effective loop quantum cosmology gives a successful description of the universe in the semiclassical region. We consider the apparent horizon of the Friedmann-Robertson-Walker universe as a thermodynamical system and investigate the thermodynamics of LQC in the semiclassical region. The effective density and effective pressure in the modified Friedmann equation from LQC not only determine the evolution of the universe in LQC scenario but also are actually found to be the thermodynamic quantities. This result comes from the energy definition in cosmology (the Misner-Sharp gravitational energy) and is consistent with thermodynamic laws. We prove that within the framework of loop quantum cosmology, the elementary equation of equilibrium thermodynamics is still valid.
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Rashkovskiy, S. A. "Hamiltonian Thermodynamics." Nelineinaya Dinamika 16, no. 4 (2020): 557–80. http://dx.doi.org/10.20537/nd200403.
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It is believed that thermodynamic laws are associated with random processes occurring in the system and, therefore, deterministic mechanical systems cannot be described within the framework of the thermodynamic approach. In this paper, we show that thermodynamics (or, more precisely, a thermodynamically-like description) can be constructed even for deterministic Hamiltonian systems, for example, systems with only one degree of freedom. We show that for such systems it is possible to introduce analogs of thermal energy, temperature, entropy, Helmholtz free energy, etc., which are related to each other by the usual thermodynamic relations. For the Hamiltonian systems considered, the first and second laws of thermodynamics are rigorously derived, which have the same form as in ordinary (molecular) thermodynamics. It is shown that for Hamiltonian systems it is possible to introduce the concepts of a thermodynamic state, a thermodynamic process, and thermodynamic cycles, in particular, the Carnot cycle, which are described by the same relations as their usual thermodynamic analogs.
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Goto, Shin-itiro. "Affine geometric description of thermodynamics." Journal of Mathematical Physics 64, no. 1 (January 1, 2023): 013301. http://dx.doi.org/10.1063/5.0124768.
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Thermodynamics provides a unified perspective of the thermodynamic properties of various substances. To formulate thermodynamics in the language of sophisticated mathematics, thermodynamics is described by a variety of differential geometries, including contact and symplectic geometries. Meanwhile, affine geometry is a branch of differential geometry and is compatible with information geometry, where information geometry is known to be compatible with thermodynamics. By combining above, it is expected that thermodynamics is compatible with affine geometry and is expected that several affine geometric tools can be introduced in the analysis of thermodynamic systems. In this paper, affine geometric descriptions of equilibrium and nonequilibrium thermodynamics are proposed. For equilibrium systems, it is shown that several thermodynamic quantities can be identified with geometric objects in affine geometry and that several geometric objects can be introduced in thermodynamics. Examples of these include the following: specific heat is identified with the affine fundamental form and a flat connection is introduced in thermodynamic phase space. For nonequilibrium systems, two classes of relaxation processes are shown to be described in the language of an extension of affine geometry. Finally, this affine geometric description of thermodynamics for equilibrium and nonequilibrium systems is compared with a contact geometric description.
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Pokrovskii, Vladimir N. "A Derivation of the Main Relations of Nonequilibrium Thermodynamics." ISRN Thermodynamics 2013 (October 21, 2013): 1–9. http://dx.doi.org/10.1155/2013/906136.
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The principles of nonequilibrium thermodynamics are discussed, using the concept of internal variables that describe deviations of a thermodynamic system from the equilibrium state. While considering the first law of thermodynamics, work of internal variables is taken into account. It is shown that the requirement that the thermodynamic system cannot fulfil any work via internal variables is equivalent to the conventional formulation of the second law of thermodynamics. These statements, in line with the axioms introducing internal variables can be considered as basic principles of nonequilibrium thermodynamics. While considering stationary nonequilibrium situations close to equilibrium, it is shown that known linear parities between thermodynamic forces and fluxes and also the production of entropy, as a sum of products of thermodynamic forces and fluxes, are consequences of fundamental principles of thermodynamics.
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WANG, LIQIU. "AN APPROACH FOR THERMODYNAMIC REASONING." International Journal of Modern Physics B 10, no. 20 (September 15, 1996): 2531–51. http://dx.doi.org/10.1142/s0217979296001124.
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Re-examination of classical thermodynamics exposes some problems. The introduction of a new reasoning approach leads to a new branch of classical thermodynamics — structural thermodynamics. An inequality principle of thermodynamic state variables decouples structure of a process set with its working medium. The introduction of optimization into thermodynamic analyses changes the attitude of classical thermodynamics from observing/describing systems to controlling/optimizing the systems. To illustrate the approach, structural thermodynamic analyses are performed for reversible heat engines and a class of irreversible heat engines. This leads to and extends the classical Carnot theory.
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Zhang, Dongliang, and Qi Ouyang. "Nonequilibrium Thermodynamics in Biochemical Systems and Its Application." Entropy 23, no. 3 (February 25, 2021): 271. http://dx.doi.org/10.3390/e23030271.
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Living systems are open systems, where the laws of nonequilibrium thermodynamics play the important role. Therefore, studying living systems from a nonequilibrium thermodynamic aspect is interesting and useful. In this review, we briefly introduce the history and current development of nonequilibrium thermodynamics, especially that in biochemical systems. We first introduce historically how people realized the importance to study biological systems in the thermodynamic point of view. We then introduce the development of stochastic thermodynamics, especially three landmarks: Jarzynski equality, Crooks’ fluctuation theorem and thermodynamic uncertainty relation. We also summarize the current theoretical framework for stochastic thermodynamics in biochemical reaction networks, especially the thermodynamic concepts and instruments at nonequilibrium steady state. Finally, we show two applications and research paradigms for thermodynamic study in biological systems.
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Shabanova, Galina, Oksana Myrgorod, Oleksandr Pirohov, and Marina Tomenko. "Barium Aluminates and the Study of their Basic Thermodynamic Data." Materials Science Forum 1100 (October 19, 2023): 139–46. http://dx.doi.org/10.4028/p-ak1mbo.
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The article presents the results of studies of thermodynamically stable barium aluminates. A database of thermodynamic data has been created: enthalpies, entropies and coefficients of the heat capacity equation, necessary for the study of multicomponent systems, including barium aluminates. Since the basis of modern materials science is multicomponent systems, on their basis it is possible to create various combinations of phases in structural materials with a set of specified properties. Thus, modern thermodynamics is not a frozen science. It is known that the objects of research are expanding, where thermodynamic methods can be applied to study the area of high and low temperatures, the area of very low and high pressures. And new discoveries give birth to new areas of application of thermodynamics: thermodynamics of thermonuclear reactions, plasma thermodynamics, relativistic thermodynamics, thermodynamics of negative absolute temperatures, etc. And, finally, the methods of thermodynamic research themselves do not remain unchanged: the exergy method, the methods of thermodynamics of irreversible processes, etc. At present, the thermodynamic method of research is widely used in various fields of physics, chemistry, biology, and many other sciences and branches of technology. Being one of the most extensive areas of modern natural science, thermodynamics plays an important role in the system of knowledge necessary for an engineer of any specialty in his practical activities. Chemical thermodynamics, on the other hand, paid the greatest attention to the study of phase transitions and the properties of solutions, and in relation to chemical reactions it was limited mainly to determining their thermal effects. To some extent, this is due to the fact that it was these areas of chemical thermodynamics that were the first to satisfy the needs of production. The practical use of known methods of thermodynamics of chemical reactions for solving major industrial problems for a long time lagged behind its capabilities.
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Quan, Hai-Tao, Hui Dong, and Chang-Pu Sun. "Theoretical and experimental progress of mesoscopic statistical thermodynamics." Acta Physica Sinica 72, no. 23 (2023): 230501. http://dx.doi.org/10.7498/aps.72.20231608.
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Does thermodynamics still hold true for mecroscopic small systems with only limited degrees of freedom? Do concepts such as temperature, entropy, work done, heat transfer, isothermal processes, and the Carnot cycle remain valid? Does the thermodynamic theory for small systems need modifying or supplementing compared with traditional thermodynamics applicable to macroscopic systems? Taking a single-particle system for example, we investigate the applicability of thermodynamic concepts and laws in small systems. We have found that thermodynamic laws still hold true in small systems at an ensemble-averaged level. After considering the information erasure of the Maxwell's demon, the second law of thermodynamics is not violated. Additionally, 'small systems' bring some new features. Fluctuations in thermodynamic quantities become prominent. In any process far from equilibrium, the distribution functions of thermodynamic quantities satisfy certain rigorously established identities. These identities are known as fluctuation theorems. The second law of thermodynamics can be derived from them. Therefore, fluctuation theorems can be considered an upgradation to the second law of thermodynamics. They enable physicists to obtain equilibrium properties (e.g. free energy difference) by measuring physical quantities associated with non-equilibrium processes (e.g. work distributions). Furthermore, despite some distinct quantum features, the performance of quantum heat engine does not outperform that of classical heat engine. The introduction of motion equations into small system makes the relationship between thermodynamics and mechanics closer than before. Physicists can study energy dissipation in non-equilibrium process and optimize the power and efficiency of heat engine from the first principle. These findings enrich the content of thermodynamic theory and provide new ideas for establishing a general framework for non-equilibrium thermodynamics.
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Tuttle, Kenneth L., and Chih Wu. "Computer-Based Thermodynamics." Journal of Educational Technology Systems 30, no. 4 (June 2002): 427–36. http://dx.doi.org/10.2190/b0x1-r5pw-lcyj-yyme.
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A new computer-based approach to teaching thermodynamics is being developed and tried by two mechanical engineering professors at the U.S. Naval Academy. The course uses sophisticated software, in this case CyclePad, to work all of the homework problems. A new text, written with traditional theory but computer-based problems, accommodates the new approach. The new course is scheduled for Fall Term 2001 at the Naval Academy. Computer-based thermodynamics courses teach the same theory as traditional thermodynamics courses as well as the same types of problems. However, traditional thermodynamic cycle hand calculations are replaced by cycle calculations using CyclePad. This new example of Intelligent Computer-Assisted Instruction, ICAI, switches emphasis from learning cycle calculations to learning cause and effect through parametric analysis. Parametric analysis is made feasible through experimentation using computer models. For this, CyclePad has artificial intelligence, sensitivity analysis and graphical presentation capabilities. Traditionally, thermodynamics culminates in analysis of the thermodynamic cycles. In this course, students will progress well beyond traditional thermodynamics courses by emphasizing cycle analysis.
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Struchtrup, Henning. "Entropy and the Second Law of Thermodynamics—The Nonequilibrium Perspective." Entropy 22, no. 7 (July 21, 2020): 793. http://dx.doi.org/10.3390/e22070793.
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An alternative to the Carnot-Clausius approach for introducing entropy and the second law of thermodynamics is outlined that establishes entropy as a nonequilibrium property from the onset. Five simple observations lead to entropy for nonequilibrium and equilibrium states, and its balance. Thermodynamic temperature is identified, its positivity follows from the stability of the rest state. It is shown that the equations of engineering thermodynamics are valid for the case of local thermodynamic equilibrium, with inhomogeneous states. The main findings are accompanied by examples and additional discussion to firmly imbed classical and engineering thermodynamics into nonequilibrium thermodynamics.
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Ruppeiner, George. "Unitary Thermodynamics from Thermodynamic Geometry." Journal of Low Temperature Physics 174, no. 1-2 (October 25, 2013): 13–34. http://dx.doi.org/10.1007/s10909-013-0949-8.
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Kolesnichenko, Aleksandr Vladimirovich. "Construction of relativistic hydrodynamics of a multicomponent fluid. 1. The method of relativistic irreversible thermodynamics." Keldysh Institute Preprints, no. 2 (2023): 1–44. http://dx.doi.org/10.20948/prepr-2023-2.
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The paper develops relativistic mechanics and irreversible thermodynamics of a cosmological liquid mixture in which thermal conduction, diffusion, viscous flow and their crossing phenomena can occur. The main thermodynamic fields that occur in relativistic irreversible thermodynamics are defined as statistical expressions using relativistic kinetics. The effects of the Eckart approach on the choice of the hydrodynamic velocity are shown. The equations of relativistic multicomponent hydrodynamics for local densities of momentum, energy and number of particles of different sort, are also obtained from the fundamental conservation laws of relativistic thermodynamics.. The energy conservation law (the first beginning of relativistic thermodynamics) is formulated. Covariant Gibbs relation and local form of the second principle of thermodynamics in the presence of entropy source were derived in order to obtain determining relations linearly connecting fluxes with corresponding thermodynamic forces. Equivalent forms of relativistic entropy production in the form of a bilinear expression in terms of thermodynamic forces were obtained. A new cross-effect between diffusion and conduction arising from the relativistic term in the thermodynamic force coupled to the heat flux is discussed. The synopsis presented is of interest for relativistic mechanics, astrophysics, and cosmology.
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TRANCOSSI, Michele, and Jose PASCOA. "Modeling Fluid dynamics and Aerodynamics by Second Law and Bejan Number (Part 1 - Theory)." INCAS BULLETIN 11, no. 3 (September 9, 2019): 169–80. http://dx.doi.org/10.13111/2066-8201.2019.11.3.15.
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Two fundamental questions are still open about the complex relation between fluid dynamics and thermodynamics. Is it possible (and convenient) to describe fluid dynamic in terms of second law based thermodynamic equations? Is it possible to solve and manage fluid dynamics problems by mean of second law of thermodynamics? This chapter analyses the problem of the relationships between the laws of fluid dynamics and thermodynamics in both first and second law of thermodynamics in the light of constructal law. In particular, taking into account constructal law and the diffusive formulation of Bejan number, it defines a preliminary step through an extensive thermodynamic vision of fluid dynamic phenomena.
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Hernández-Lemus, Enrique. "Nonequilibrium Thermodynamics of Cell Signaling." Journal of Thermodynamics 2012 (July 30, 2012): 1–10. http://dx.doi.org/10.1155/2012/432143.
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Signal transduction inside and across the cells, also called cellular signaling, is key to most biological functions and is ultimately related with both life and death of the organisms. The processes giving rise to the propagation of biosignals are complex and extremely cooperative and occur in a far-from thermodynamic equilibrium regime. They are also driven by activation kinetics strongly dependent on local energetics. For these reasons, a nonequilibrium thermodynamical description, taking into account not just the activation of second messengers, but also transport processes and dissipation is desirable. Here we present a proposal for such a formalism, that considers cells as small thermodynamical systems and incorporates the role of fluctuations as intrinsic to the dynamics in a spirit guided by mesoscopic nonequilibrium thermodynamics. We present also a minimal model for cellular signaling that includes contributions from activation, transport, and intrinsic fluctuations. We finally illustrate its feasibility by considering the case of FAS signaling which is a vital signal transduction pathway that determines either cell survival or death by apoptosis.
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Haldar, Sourav, Pritikana Bhandari, and Subenoy Chakraborty. "A thermodynamical analysis of the inhomogeneous FLRW type model: Redefined Bekenstein–Hawking system." International Journal of Geometric Methods in Modern Physics 14, no. 11 (October 23, 2017): 1750159. http://dx.doi.org/10.1142/s0219887817501596.
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A detailed thermodynamical study has been presented for the inhomogeneous FLRW-type model of the Universe bounded by a horizon with three possible modifications of Bekenstein–Hawking formulation of thermodynamical parameters namely entropy and temperature. For the first choice of the thermodynamical system validity of both the first law of thermodynamics (FLT) and the generalized second law of thermodynamics (GSLT) are examined. Also, the integrability conditions for the exact one-forms in both the thermodynamical laws are analyzed and it is found that they are consistent with each other. On the other hand, for the other two choices of the thermodynamical system to hold the first law of thermodynamics, one must restrict the parameters (in the definition of the thermodynamical variables) in some specific integral form.
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Wulandari, Dewi, Destria Roza, M. Aswin Rangkuti, Yul Ifda Tanjung, and Irham Ramadhani. "THE LEVEL UNDERSTANDING OF THERMODYNAMIC CONCEPT FOR PHYSICS AND CHEMISTRY UNDERGRADUATE STUDENTS." Jurnal Pendidikan Fisika 12, no. 1 (June 4, 2023): 1. http://dx.doi.org/10.24114/jpf.v12i1.42330.
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Thermodynamics is an abstract concept making it difficult for physics and chemistry undergraduate student to understand it. The purpose of this research is to know the level understanding of the fundamental concepts of thermodynamics so that lecturers can develop strategies to teach thermodynamics appropriately. An exploratory small-scale study was conducted on students majoring in physics and chemistry to evaluate an understanding of heat, temperature, energy, work, thermodynamic processes and the first law of thermodynamics. The research sample consisted of 20 undergraduate students who were randomly selected from two majors, namely physics and chemistry. Data were collected through a diagnostic test to determine the level understanding of students' concepts which consisted of 20 questions. In addition, interviews were conducted with those of 20 students related to given questions. The results showed that the level of students' conceptual understanding of the concept of thermodynamics was still low. The main reasons that cause students have problems in understanding thermodynamic concepts are the concept of thermodynamics is an abstract physics concept and the matters of thermodynamics are lack in explanation and interpretation of phenomena and not linking them to daily life
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Végh, Ádám, Csaba Mekler, and György Kaptay. "A Unified Theoretical Framework to Model Bulk, Surface and Interfacial Thermodynamic Properties of Immiscible Liquid Alloys." Materials Science Forum 752 (March 2013): 10–19. http://dx.doi.org/10.4028/www.scientific.net/msf.752.10.
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Bulk, surface and interface thermodynamics of immiscible liquid alloys are considered within a unified theoretical framework. For bulk thermodynamic functions the exponential and the combined linear-exponential equations are discussed, obeying the 4th law of thermodynamics. Surface phase transition is discussed in details. For surface and interface thermodynamics the monolayer Butler equation is compared to the multilayer model. During further assessment of bulk thermodynamic data of immiscible liquid alloys their experimentally measured surface tension and interfacial energy should be also taken into account, coupled with the models presented here.
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Kruglov, Sergey Il’ich. "AdS Black Holes in the Framework of Nonlinear Electrodynamics, Thermodynamics, and Joule–Thomson Expansion." Symmetry 14, no. 8 (August 3, 2022): 1597. http://dx.doi.org/10.3390/sym14081597.
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The thermodynamics and phase transitions of magnetic Anti-de Sitter black holes were studied. We considered extended-phase-space thermodynamics, with the cosmological constant being a thermodynamic pressure and the black hole mass being treated as a chemical enthalpy. The extended-phase-space thermodynamics of black holes mimic the behavior of a Van der Waals liquid. Quantities conjugated to the coupling of nonlinear electrodynamics (NED) and a magnetic charge are obtained. Thermodynamic critical points of phase transitions are investigated. It was demonstrated that the first law of black hole thermodynamics and the generalized Smarr relation hold. The Joule–Thomson adiabatic expansion of NED-AdS black holes is studied. The dependence of inversion temperature on pressure and the minimum of the inversion temperature are found.
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BADESCU, VIOREL. "PHYSICAL TEMPERATURE AND PRESSURE IN FULLY NONEXTENSIVE STATISTICAL THERMODYNAMICS." Advances in Complex Systems 11, no. 01 (February 2008): 43–54. http://dx.doi.org/10.1142/s0219525908001477.
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This paper generalizes previous results concerning the definitions of physical temperature and pressure in nonextensive statistical thermodynamics. The novelty is that both the internal energy and the volume are no longer additive functions. The new approach is referred to as "fully" nonextensive thermodynamics. The physical temperature is different from the inverse of the Lagrange multiplier. This fact changes the form of some usual thermodynamic relations. For example, the Clausius definition of the thermodynamic entropy has to be modified. As an application, the classical gas model is examined with statistical calculations performed under the Tsallis–Mendes–Plastino formalism of nonextensive thermodynamics. The specific heat expression differs from the one encountered in ordinary extensive thermodynamics but the equation of state keeps the same form.
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Jawad, Abdul, Sadaf Butt, and Aneesa Majeed. "Thermodynamics of squared speed of sound parametrizations." International Journal of Geometric Methods in Modern Physics 17, no. 05 (April 2020): 2050072. http://dx.doi.org/10.1142/s0219887820500723.
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In this work, an attempt is made to study the thermodynamical analysis at the apparent horizon in the framework of fractal universe. We consider the Bekenstein entropy to examine validity of the generalized second law of thermodynamics (GSLT) and thermal equilibrium for the four different cases which are developed with the utilization of different forms of squared speed of sound. In each case, we explore the behavior of total entropy through the graphical variation of its first- and second-order derivatives with respect to redshift parameter ([Formula: see text]). It is found that generalized second law of thermodynamics holds for Cases 1 and 2 for [Formula: see text] and [Formula: see text], respectively and it holds in late times as well. However, for Cases [Formula: see text] and [Formula: see text], this law is satisfied in early, present and future epochs. Furthermore, for Cases 1 and 2, instability of thermodynamic equilibrium is observed, but for Cases 3 and 4, it holds in the specific intervals [Formula: see text] and [Formula: see text], respectively.
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Gao, Zeyuan, and Liu Zhao. "Restricted phase space thermodynamics for AdS black holes via holography." Classical and Quantum Gravity 39, no. 7 (March 11, 2022): 075019. http://dx.doi.org/10.1088/1361-6382/ac566c.
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Abstract A new formalism for thermodynamics of AdS black holes called the restricted phase space thermodynamics (RPST) is proposed. The construction is based on top of Visser’s holographic thermodynamics, but with the AdS radius fixed as a constant. Thus the RPST is free of the (P, V) variables but inherits the central charge and chemical potential as a new pair of conjugate thermodynamic variables. In this formalism, the Euler relation and the Gibbs–Duhem equation hold simultaneously with the first law of black hole thermodynamics, which guarantee the appropriate homogeneous behaviors for the black hole mass and the intensive variables. The formalism is checked in detail in the example case of four-dimensional Reissner–Nordström anti-de Sitter black hole in Einstein–Maxwell theory, in which some interesting thermodynamic behaviors are revealed.
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Glasser, Leslie, and H. Donald Brooke Jenkins. "Predictive thermodynamics for ionic solids and liquids." Physical Chemistry Chemical Physics 18, no. 31 (2016): 21226–40. http://dx.doi.org/10.1039/c6cp00235h.
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Sharif, M., and Sara Ashraf. "Thermodynamics of Modified Cosmic Chaplygin Gas." Advances in High Energy Physics 2018 (October 3, 2018): 1–8. http://dx.doi.org/10.1155/2018/8949252.
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We examine the thermodynamic features of an exotic fluid known as modified cosmic Chaplygin gas in the context of homogeneous isotropic universe model. For this purpose, the behavior of physical parameters is discussed that help to analyze nature of the universe. Using specific heat formalism, the validity of third law of thermodynamics is checked. Furthermore, with the help of thermodynamic entities, the thermal equation of state is also discussed. The thermodynamic stability is explored by means of adiabatic, specific heat and isothermal conditions from classical thermodynamics. It is concluded that the considered fluid configuration is thermodynamically stable and expands adiabatically for an appropriate choice of parameters.
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Guo, Lina, and Jiulin Du. "Thermodynamic potentials and thermodynamic relations in nonextensive thermodynamics." Physica A: Statistical Mechanics and its Applications 390, no. 2 (January 2011): 183–88. http://dx.doi.org/10.1016/j.physa.2010.09.021.
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Matsoukas, Themis. "Thermodynamics Beyond Molecules: Statistical Thermodynamics of Probability Distributions." Entropy 21, no. 9 (September 13, 2019): 890. http://dx.doi.org/10.3390/e21090890.
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Statistical thermodynamics has a universal appeal that extends beyond molecular systems, and yet, as its tools are being transplanted to fields outside physics, the fundamental question, what is thermodynamics, has remained unanswered. We answer this question here. Generalized statistical thermodynamics is a variational calculus of probability distributions. It is independent of physical hypotheses but provides the means to incorporate our knowledge, assumptions and physical models about a stochastic processes that gives rise to the probability in question. We derive the familiar calculus of thermodynamics via a probabilistic argument that makes no reference to physics. At the heart of the theory is a space of distributions and a special functional that assigns probabilities to this space. The maximization of this functional generates the mathematical network of thermodynamic relationship. We obtain statistical mechanics as a special case and make contact with Information Theory and Bayesian inference.
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Siagian, Ruben Cornelius, Lulut Alfaris, Arip Nurahman, and Eko Pramesti Sumarto. "TERMODINAMIKA LUBANG HITAM: HUKUM PERTAMA DAN KEDUA SERTA PERSAMAAN ENTROPI." Jurnal Kumparan Fisika 6, no. 1 (May 11, 2023): 1–10. http://dx.doi.org/10.33369/jkf.6.1.1-10.
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ABSTRAK Artikel ini membahas konsep termodinamika yang berlaku pada Lubang Hitam, yaitu hukum termodinamika pertama dan kedua. Hukum pertama termodinamika menghubungkan perubahan massa dengan perubahan entropi dan kerja, memungkinkan Lubang Hitam diperlakukan sebagai sistem termodinamika dengan suhu dan entropi. Hukum kedua termodinamika menyatakan bahwa entropi suatu sistem terisolasi dalam kesetimbangan termodinamika selalu meningkat atau tetap konstan, termasuk untuk Lubang Hitam. Metode penulisan yang digunakan dalam artikel ini melibatkan derivasi matematis untuk entropi Lubang Hitam, dengan menggabungkan hukum kedua termodinamika dan konsep termodinamika Lubang Hitam, di mana entropi dapat dinyatakan sebagai fungsi luas cakrawala peristiwa. Artikel ini menyoroti pentingnya konsep entropi dan termodinamika Lubang Hitam dalam memahami alam semesta, serta penerapannya di berbagai bidang sains. Kata kunci—Lubang Hitam, Termodinamika, Entropi, Hukum pertama termodinamika, Hukum kedua termodinamika ABSTRACT This article delves into the concepts of thermodynamics that apply to Lubang Hitams, namely the first and second laws of thermodynamics. The first law of thermodynamics connects changes in mass with changes in entropy and work, allowing Lubang Hitams to be treated as thermodynamic systems with temperature and entropy. The second law of thermodynamics states that the entropy of an isolated system in thermodynamic equilibrium always increases or remains constant, including for Lubang Hitams. The writing approach employed in this article involves mathematical derivations for Lubang Hitam entropy, combining the second law of thermodynamics with the concept of Lubang Hitam thermodynamics, where entropy can be expressed as a function of the event horizon's surface area. This article highlights the significance of entropy and Lubang Hitam thermodynamics in understanding the universe, as well as their applications in various scientific fields. Keywords—Lubang Hitam, Thermodynamics, Entropy, First law of thermodynamics, Second law of thermodynamics
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Gyftopoulos, Elias P. "Entropies of Statistical Mechanics and Disorder Versus the Entropy of Thermodynamics and Order." Journal of Energy Resources Technology 123, no. 2 (December 13, 2000): 110–18. http://dx.doi.org/10.1115/1.1368122.
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The prevailing beliefs in the scientific and engineering literature are that: (i) thermodynamics is explained and justified by statistical mechanics; (ii) entropy is a statistical measure of disorder; and (iii) for given values of energy, volume, and amounts of constituents, the largest value of entropy corresponds to both a thermodynamic equilibrium state and the ultimate disorder. In this paper, we provide: (i) a summary of the beliefs as stated by some eminent scientists; (ii) experimental evidence that casts serious doubt about the validity of the beliefs; (iii) an outline of a nonstatistical unified quantum theory of mechanics and thermodynamics; (iv) an outline of a nonquantal, nonstatistical exposition of thermodynamics, valid for all systems (both macroscopic and microscopic), and for all states (both thermodynamic equilibrium and not thermodynamic equilibrium); (v) the definition and analytical expression of the entropy of thermodynamics; (vi) the interpretation of entropy as both a measure of the quantum-theoretic spatial shape of a molecule, and an indicator of order; and (vii) nonstatistical answers to the questions that motivated the introduction of statistical mechanics.
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Tovbin, Yu K. "Second Law of Thermodynamics, Gibbs’ Thermodynamics, and Relaxation Times of Thermodynamic Parameters." Russian Journal of Physical Chemistry A 95, no. 4 (April 2021): 637–58. http://dx.doi.org/10.1134/s0036024421020266.
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Čička, Roman. "Applications of Computational Thermodynamics in Materials Science Courses." Research Papers Faculty of Materials Science and Technology Slovak University of Technology 30, no. 51 (November 1, 2022): 1–8. http://dx.doi.org/10.2478/rput-2022-0010.
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Abstract Computational thermodynamics is an important tool used to predict the phase equilibria, phase compositions, transformation temperatures, solubility limits and many thermodynamic properties of multi-component materials. In this contribution, the possibilities of how to introduce computational thermodynamics into the university Materials Science courses using Thermo-Calc software are described. Also, the application of computational thermodynamics in materials research and development of new materials is shortly outlined.
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Seifert, Udo. "From Stochastic Thermodynamics to Thermodynamic Inference." Annual Review of Condensed Matter Physics 10, no. 1 (March 10, 2019): 171–92. http://dx.doi.org/10.1146/annurev-conmatphys-031218-013554.
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For a large class of nonequilibrium systems, thermodynamic notions like work, heat, and, in particular, entropy production can be identified on the level of fluctuating dynamical trajectories. Within stochastic thermodynamics various fluctuation theorems relating these quantities have been proven. Their application to experimental systems requires that all relevant mesostates are accessible. Recent advances address the typical situation that only partial, or coarse-grained, information about a system is available. Thermodynamic inference as a general strategy uses consistency constraints derived from stochastic thermodynamics to infer otherwise hidden properties of nonequilibrium systems. An important class in this respect are active particles, for which we resolve the conflicting strategies that have been proposed to identify entropy production. As a paradigm for thermodynamic inference, the thermodynamic uncertainty relation provides a lower bound on the entropy production through measurements of the dispersion of any current in the system. Likewise, it quantifies the cost of precision for biomolecular processes. Generalizations and ramifications allow the inference of, inter alia, model-free upper bounds on the efficiency of molecular motors and of the minimal number of intermediate states in enzymatic networks.
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de Miguel, Rodrigo, and J. Miguel Rubí. "Thermodynamics Far from the Thermodynamic Limit." Journal of Physical Chemistry B 121, no. 45 (November 7, 2017): 10429–34. http://dx.doi.org/10.1021/acs.jpcb.7b08621.
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Andresen, Bjarne. "Finite-time thermodynamics and thermodynamic length." Revue Générale de Thermique 35, no. 418-419 (November 1996): 647–50. http://dx.doi.org/10.1016/s0035-3159(96)80060-2.
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Dolan, Brian P. "Black holes and Boyle's law — The thermodynamics of the cosmological constant." Modern Physics Letters A 30, no. 03n04 (January 30, 2015): 1540002. http://dx.doi.org/10.1142/s0217732315400027.
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When the cosmological constant, Λ, is interpreted as a thermodynamic variable in the study of black hole thermodynamics a very rich structure emerges. It is natural to interpret Λ as a pressure and define the thermodynamically conjugate variable to be the thermodynamic volume of the black hole (which need not bear any relation to the geometric volume). Recent progress in this new direction for black hole thermodynamics is reviewed.
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Megías, Eugenio, Airton Deppman, Tobias Frederico, and Débora P. Menezes. "Fractal structure of hadrons and non-extensive statistics*." EPJ Web of Conferences 192 (2018): 00046. http://dx.doi.org/10.1051/epjconf/201819200046.
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The role played by non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Some possible mechanisms that could give rise to non-extensive statistics have been formulated along the last few years, in particular the existence of a fractal structure in thermodynamic functions for hadronic systems. We investigate the properties of such fractal thermodynamical systems, in particular the fractal scale invariance is discussed in terms of the Callan-Symanzik equation. Finally, we propose a diagrammatic method for calculations of relevant quantities.
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Maikov, V. P., and A. I. Balunov. "Nonlocal approach to thermodynamics of mixtures." Izvestiya MGTU MAMI 7, no. 1-4 (July 10, 2013): 176–81. http://dx.doi.org/10.17816/2074-0530-67882.
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The paper examines the highlights of mixture theory on the basis of generalized nonlocal (discrete) thermodynamics that involves Shannon entropy. Generalization of the equilibrium thermodynamics is obtained basing on the hypothesis of quantized entropy. The paper defines the elemental macroscopic thermodynamics space that serves as the basis of the mixture theory. The theory allows to use generalized thermodynamic method instead of empirical equations including laws of Raul and Dalton.
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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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Haldar, Amritendu, and Ritabrata Biswas. "Thermodynamics of d-dimensional charged AdS (Anti-de sitter) black holes: Hamiltonian approach and Clapeyron equation." Modern Physics Letters A 34, no. 22 (July 20, 2019): 1950170. http://dx.doi.org/10.1142/s0217732319501700.
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The study of thermodynamics in the view of the Hamiltonian approach is the newest tool to analyze the thermodynamic properties of the black holes (BHs). In this paper, we investigate the thermodynamics of d-dimensional [Formula: see text] asymptotically Anti-de Sitter (AdS) BHs. A thermodynamic representation based on symplectic geometry is introduced in this paper. We extend the thermodynamics of d-dimensional charged AdS BHs in the views of a Hamiltonian approach. Firstly, we study the thermodynamics in reduced phase space and correlate with the Schwarzschild solution. Then we enhance it in the extended phase space. In an extended phase space, the thermodynamic equations of state are stated as constraints. We apply the canonical transformation to analyze the thermodynamics of the said type of BHs. We plot [Formula: see text]-[Formula: see text] diagrams for different dimensions d taking the temperatures [Formula: see text], [Formula: see text] and [Formula: see text] and analyze the natures of the graphs and the dependences on d. In these diagrams, we point out the regions of coexistence. We also examine the phase transition by applying “Maxwell’s equal area law” of the said BHs. Here, we find the regions of coexistence of two phases which are also depicted graphically. Finally, we derive the “Clapeyron equation” and investigate the latent heat of isothermal phase transition.
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Yovan, Ricki Angga Rizti, Intan Sumarak Ningsari, Adhelia Karunia Sukma, Yuyun Nailul Qomariah, and Hasan Nuurul Hidayaatullaah. "Analysis of Physics University Students' Knowledge and Understanding of Thermodynamic Scientists." Studies in Philosophy of Science and Education 2, no. 1 (May 24, 2021): 17–23. http://dx.doi.org/10.46627/sipose.v2i1.59.
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This study aims to determine the knowledge and understanding of physics students related to thermodynamic scientists. This research method is descriptive quantitative and qualitative. Collecting data using a google form-based test instrument with 3 levels of questions on six scientist figures, namely Joseph Black, Robert Boyle, Joseph Louis Gay Lussac, Sadi Carnot, James Presscout Joule, and Gabriel Fahrenheit. The subjects of this research were students of physics at the State University of Surabaya in levels one and two who had taken basic physics courses. Based on research data, the percentage of respondents understanding related to thermodynamics, namely 12% did not know thermodynamics scientists, 24% only knew thermodynamics scientists, 40% understood the concept of thermodynamic scientists sufficiently, 24% understood the concept and could explain the concept of thermodynamic scientists findings as a whole. University students' knowledge and understanding related to thermodynamic scientists are mostly at the level of understanding. The most widely known figure of thermodynamic scientists and the concept of the most widely understood is Robert Boyle and the most unknown is Joseph Louis Gay Lussac.
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Feistel, Rainer, and Olaf Hellmuth. "Irreversible Thermodynamics of Seawater Evaporation." Journal of Marine Science and Engineering 12, no. 1 (January 15, 2024): 166. http://dx.doi.org/10.3390/jmse12010166.
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Under typical marine conditions of about 80% relative humidity, evaporation of water from the ocean is an irreversible process accompanied by entropy production. In this article, equations are derived for the latent heat of irreversible evaporation and the related nonequilibrium entropy balance at the sea surface. To achieve this, linear irreversible thermodynamics is considered in a conceptual ocean evaporation model. The equilibrium thermodynamic standard TEOS-10, the International Thermodynamic Equation of Seawater—2010, is applied to irreversible evaporation under the assumption of local thermodynamic equilibrium. The relevance of local equilibrium conditions for irreversible thermodynamics is briefly explained. New equations are derived for the mass flux of evaporation and for the associated nonequilibrium enthalpies and entropies. The estimated entropy production rate of ocean evaporation amounts to 0.004 W m−2 K−1 as compared with the average terrestrial global entropy production of about 1 W m−2 K−1.
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Ma, Meng-Sen, Yan-Song Liu, and Huai-Fan Li. "Revisit on the thermodynamic stability of the noncommutative Schwarzschild black hole." International Journal of Modern Physics D 26, no. 03 (February 3, 2017): 1750018. http://dx.doi.org/10.1142/s0218271817500183.
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In two frameworks, we discuss the thermodynamic stability of noncommutative geometry inspired Schwarzschild black hole (NCSBH). Under the horizon thermodynamics of black holes, we show that the NCSBH cannot be thermodynamically stable if requiring positive temperature. We note the inconsistency in the work of Larrañaga et al. and propose an effective first law of black hole thermodynamics for the NCSBH to eliminate the inconsistency. Based on the effective first law, we recalculate the heat capacity and the thermodynamic curvature by means of geometrothermodynamics (GTD) to revisit the thermodynamic stability.
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Vincze, Gy, and A. Szasz. "Critical analysis of the thermodynamics of reaction kinetics." JOURNAL OF ADVANCES IN PHYSICS 10, no. 1 (August 5, 2015): 2538–59. http://dx.doi.org/10.24297/jap.v10i1.1340.
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Our objective is to show the weakness of the recent thermodynamics of chemical reactions. We show that such a thermodynamic theory of chemical reactions, which could be similar to the generalized Onsager’s theory in thermodynamics, is not reality at the moment.Â
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Zhou, Chenxi, Bin Yang, Wenliang Fan, and Wei Li. "Brain Model Based on the Canonical Ensemble with Functional MRI: A Thermodynamic Exploration of the Neural System." Complexity 2021 (December 21, 2021): 1–12. http://dx.doi.org/10.1155/2021/9961864.
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Objective. System modeling is an important method to study the working mechanisms of the brain. This study attempted to build a model of the brain from the perspective of thermodynamics at the system level, which brought a new perspective to brain modeling. Approach. Regarding brain regions as systems, voxels as particles, and intensity of signals as energy of particles, the thermodynamic model of the brain was built based on the canonical ensemble theory. Two pairs of activated regions and two pairs of inactivated brain regions were selected for comparison in this study, and the thermodynamic properties based on the proposed model were analyzed. In addition, the thermodynamic properties were extracted as input features for the detection of Alzheimer’s disease. Main Results. The experimental results verified the assumption that the brain follows thermodynamic laws. This demonstrated the feasibility and rationality of the proposed brain thermodynamic modeling method, indicating that thermodynamic parameters drawn from our model can be applied to describe the state of the neural system. Meanwhile, the brain thermodynamic model achieved good accuracy in the detection of Alzheimer’s disease, suggesting the potential application of thermodynamic models in auxiliary diagnosis. Significance. (1) In the previous studies, only some thermodynamic parameters in physics were analogized and applied to brain image analysis, while, in this study, a complete system model of the brain was proposed through the principles of thermodynamics. And, based on the neural system models proposed, thermodynamic parameters were obtained to describe the observation and evolution of the neural system. (2) Based on the proposed thermodynamic models, we found and confirmed that the neural system also follows the laws of thermodynamics: the activation of system always leads to increased internal energy, increased free energy, and decreased entropy as what is discovered in many other systems besides classic thermodynamic system. (3) The detection of neural disease was demonstrated to benefit from the thermodynamic model, which confirmed that the thermodynamic model proposed can indeed describe the evolution of the neural system diseases. And it further implied the immense potential of thermodynamics in auxiliary diagnosis.
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Bécar, Ramón, P. A. González, Joel Saavedra, Yerko Vásquez, and Bin Wang. "Phase transitions in four-dimensional AdS black holes with a nonlinear electrodynamics source." Communications in Theoretical Physics 73, no. 12 (November 12, 2021): 125402. http://dx.doi.org/10.1088/1572-9494/ac3073.
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Abstract In this work we consider black hole solutions to Einstein’s theory coupled to a nonlinear power-law electromagnetic field with a fixed exponent value. We study the extended phase space thermodynamics in canonical and grand canonical ensembles, where the varying cosmological constant plays the role of an effective thermodynamic pressure. We examine thermodynamical phase transitions in such black holes and find that both first- and second-order phase transitions can occur in the canonical ensemble while, for the grand canonical ensemble, Hawking–Page and second-order phase transitions are allowed.
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Schmitz, Georg J., Michael te Vrugt, Tore Haug-Warberg, Lodin Ellingsen, Paul Needham, and Raphael Wittkowski. "Thermodynamics of an Empty Box." Entropy 25, no. 2 (February 8, 2023): 315. http://dx.doi.org/10.3390/e25020315.
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A gas in a box is perhaps the most important model system studied in thermodynamics and statistical mechanics. Usually, studies focus on the gas, whereas the box merely serves as an idealized confinement. The present article focuses on the box as the central object and develops a thermodynamic theory by treating the geometric degrees of freedom of the box as the degrees of freedom of a thermodynamic system. Applying standard mathematical methods to the thermodynamics of an empty box allows equations with the same structure as those of cosmology and classical and quantum mechanics to be derived. The simple model system of an empty box is shown to have interesting connections to classical mechanics, special relativity, and quantum field theory.
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Sheykhi, Ahmad. "Thermodynamics of apparent horizon in mimetic cosmology." International Journal of Modern Physics D 28, no. 03 (February 2019): 1950057. http://dx.doi.org/10.1142/s0218271819500573.
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A new perspective toward Einstein’s theory of general relativity, called mimetic gravity, was suggested in [A. H. Chamseddine and V. Mukhanov, J. High Energy Phys. 1311 (2013) 135] by isolating the conformal degree of freedom in a covariant fashion through a re-parametrization of the physical metric in terms of an auxiliary metric and a mimetic field. In this paper, we first derive the Friedmann equations of the Friedmann–Robertson–Walker (FRW) universe with any spatial curvature in mimetic gravity. Then, we disclose that one can always rewrite the Friedmann equations of mimetic cosmology in the form of the first law of thermodynamics, [Formula: see text], on the apparent horizon. We confirm that the entropy associated with the apparent horizon in mimetic cosmology still obeys the area law of entropy which is useful in studying the thermodynamical properties of the black holes in mimetic gravity. We also examine the time evolution of the total entropy in mimetic cosmology and show that, with the local equilibrium assumption, the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon. Our study further supports the viability of the mimetic gravity from a thermodynamic viewpoint and provides a strong consistency check of this model.
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Wampler, Taylor, and Andre C. Barato. "Skewness and kurtosis in stochastic thermodynamics." Journal of Physics A: Mathematical and Theoretical 55, no. 1 (December 9, 2021): 014002. http://dx.doi.org/10.1088/1751-8121/ac3b0c.
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Abstract The thermodynamic uncertainty relation is a prominent result in stochastic thermodynamics that provides a bound on the fluctuations of any thermodynamic flux, also known as current, in terms of the average rate of entropy production. Such fluctuations are quantified by the second moment of the probability distribution of the current. The role of higher order standardized moments such as skewness and kurtosis remains largely unexplored. We analyze the skewness and kurtosis associated with the first passage time of thermodynamic currents within the framework of stochastic thermodynamics. We develop a method to evaluate higher order standardized moments associated with the first passage time of any current. For systems with a unicyclic network of states, we conjecture upper and lower bounds on skewness and kurtosis associated with entropy production. These bounds depend on the number of states and the thermodynamic force that drives the system out of equilibrium. We show that these bounds for skewness and kurtosis do not hold for multicyclic networks. We discuss the application of our results to infer an underlying network of states.
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Cimmelli, Vito Antonio, and Patrizia Rogolino. "The Role of the Second Law of Thermodynamics in Continuum Physics: A Muschik and Ehrentraut Theorem Revisited." Symmetry 14, no. 4 (April 7, 2022): 763. http://dx.doi.org/10.3390/sym14040763.
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In continuum physics, constitutive equations model the material properties of physical systems. In those equations, material symmetry is taken into account by applying suitable representation theorems for symmetric and/or isotropic functions. Such mathematical representations must be in accordance with the second law of thermodynamics, which imposes that, in any thermodynamic process, the entropy production must be nonnegative. This requirement is fulfilled by assigning the constitutive equations in a form that guaranties that second law of thermodynamics is satisfied along arbitrary processes. Such an approach, in practice regards the second law of thermodynamics as a restriction on the constitutive equations, which must guarantee that any solution of the balance laws also satisfy the entropy inequality. This is a useful operative assumption, but not a consequence of general physical laws. Indeed, a different point of view, which regards the second law of thermodynamics as a restriction on the thermodynamic processes, i.e., on the solutions of the system of balance laws, is possible. This is tantamount to assuming that there are solutions of the balance laws that satisfy the entropy inequality, and solutions that do not satisfy it. In order to decide what is the correct approach, Muschik and Ehrentraut in 1996, postulated an amendment to the second law, which makes explicit the evident (but rather hidden) assumption that, in any point of the body, the entropy production is zero if, and only if, this point is a thermodynamic equilibrium. Then they proved that, given the amendment, the second law of thermodynamics is necessarily a restriction on the constitutive equations and not on the thermodynamic processes. In the present paper, we revisit their proof, lighting up some geometric aspects that were hidden in therein. Moreover, we propose an alternative formulation of the second law of thermodynamics, which incorporates the amendment. In this way we make this important result more intuitive and easily accessible to a wider audience.
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Bergmann, Nicolas, and Michael Galperin. "A Green’s function perspective on the nonequilibrium thermodynamics of open quantum systems strongly coupled to baths." European Physical Journal Special Topics 230, no. 4 (April 12, 2021): 859–66. http://dx.doi.org/10.1140/epjs/s11734-021-00067-3.
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AbstractWe give a nonequilibrium Green’s function (NEGF) perspective on thermodynamics formulations for open quantum systems that are strongly coupled to baths. A scattering approach implying thermodynamic consideration of a supersystem (system plus baths) that is weakly coupled to external superbaths is compared with the consideration of thermodynamics of a system that is strongly coupled to its baths. We analyze both approaches from the NEGF perspective and argue that the latter yields a possibility of thermodynamic formulation consistent with a dynamical (quantum transport) description.
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Sevilla, Francisco J. "Thermodynamics of Low-Dimensional Trapped Fermi Gases." Journal of Thermodynamics 2017 (January 26, 2017): 1–12. http://dx.doi.org/10.1155/2017/3060348.
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The effects of low dimensionality on the thermodynamics of a Fermi gas trapped by isotropic power-law potentials are analyzed. Particular attention is given to different characteristic temperatures that emerge, at low dimensionality, in the thermodynamic functions of state and in the thermodynamic susceptibilities (isothermal compressibility and specific heat). An energy-entropy argument that physically favors the relevance of one of these characteristic temperatures, namely, the nonvanishing temperature at which the chemical potential reaches the Fermi energy value, is presented. Such an argument allows interpreting the nonmonotonic dependence of the chemical potential on temperature, as an indicator of the appearance of a thermodynamic regime, where the equilibrium states of a trapped Fermi gas are characterized by larger fluctuations in energy and particle density as is revealed in the corresponding thermodynamics susceptibilities.
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Samohýl, Vít, Ivan Samohýl, and Petr Voňka. "Partial Pressures in Thermodynamics of Classical Fluid Mixtures." Acta Chimica Slovaca 5, no. 1 (April 1, 2012): 29–36. http://dx.doi.org/10.2478/v10188-012-0005-3.
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Partial Pressures in Thermodynamics of Classical Fluid Mixtures In the rational thermodynamics of most usual nonequilibrium "classical" fluid mixtures it has been proposed the "thermodynamic" partial pressure which generalize traditional definitions and merge together in an ideal gas mixture. In this paper, these thermodynamic partial pressures are calculated for a (real) gas mixture of methane-ethane-carbon dioxide and a liquid mixture of lithium hydroxide in water. The results are compared with those obtained using the classical formulations of partial pressures calculated in these mixtures as well.