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Journal articles on the topic 'Non-equilibrium thermodynamics'

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1

Maity, Subhayan. "Non-Equilibrium Thermodynamics in the Non-Canonical Scalar Field Perturbed Space-Time: Stability Analysis." Open Access Journal of Astronomy 2, no. 1 (2024): 1–8. http://dx.doi.org/10.23880/oaja-16000115.

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The space-time of the Universe has been perturbed under a scalar field ϕ considering the minimum coupling between and the background metric. The solutions of Einstein field equations have been obtained under perturbed geometry and the corresponding conservation equation shows the non-equilibrium thermodynamic prescription of the cosmic fluid. Following the stability criteria of the cosmic fluid along with the laws of thermodynamics, some constraints have been imposed on the choice of ϕ.
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2

Igamberdiev, Abir U. "Toward the Relational Formulation of Biological Thermodynamics." Entropy 26, no. 1 (December 31, 2023): 43. http://dx.doi.org/10.3390/e26010043.

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Classical thermodynamics employs the state of thermodynamic equilibrium, characterized by maximal disorder of the constituent particles, as the reference frame from which the Second Law is formulated and the definition of entropy is derived. Non-equilibrium thermodynamics analyzes the fluxes of matter and energy that are generated in the course of the general tendency to achieve equilibrium. The systems described by classical and non-equilibrium thermodynamics may be heuristically useful within certain limits, but epistemologically, they have fundamental problems in the application to autopoietic living systems. We discuss here the paradigm defined as a relational biological thermodynamics. The standard to which this refers relates to the biological function operating within the context of particular environment and not to the abstract state of thermodynamic equilibrium. This is defined as the stable non-equilibrium state, following Ervin Bauer. Similar to physics, where abandoning the absolute space-time resulted in the application of non-Euclidean geometry, relational biological thermodynamics leads to revealing the basic iterative structures that are formed as a consequence of the search for an optimal coordinate system by living organisms to maintain stable non-equilibrium. Through this search, the developing system achieves the condition of maximization of its power via synergistic effects.
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3

de Hemptinne, X. "Non-equilibrium statistical thermodynamics." Journal of Molecular Liquids 67 (December 1995): 71–80. http://dx.doi.org/10.1016/0167-7322(95)00867-5.

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4

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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5

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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6

Zhou, Xiao-Dong. "(Invited) On Non-equilibrium Thermodynamics in Electrochemical Systems." ECS Meeting Abstracts MA2023-02, no. 46 (December 22, 2023): 2268. http://dx.doi.org/10.1149/ma2023-02462268mtgabs.

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Much of our understanding of physical behavior of materials is based on the concept of equilibrium, which lies at the heart of classical thermodynamics, condensed matter physics, and modern reaction kinetics. If a thermodynamic system is in equilibrium conditions, which is the situation when an energy system (e.g., a fuel cell or a battery) is under open circuit voltage, the surface and bulk of the electrode are only subject to fluctuation of thermodynamic qualities. For the cases that are not at equilibrium, but are close to it, Onsager established linear reciprocal relationships between flux and thermodynamic force for a thermodynamic system in nonequilibrium states. These linear relationships are manifested in transport phenomena, which are non-equilibrium processes, such as ion diffusion and heat conduction. When an electrochemical reaction takes place at an electrode of a fuel cell, electrolyzer, or battery, the thermodynamic system is far away from equilibrium. Therefore, the thermodynamic states of the surface and bulk of an electrode are subject to external thermodynamic forces. As a result, in an active electrode, the electrochemical reaction on the surface causes all thermodynamic variables to change in both the surface and the bulk. In this talk, I will use solid oxide cells and lithium-ion batteries as an example to address three questions related to materials in non-equilibrium thermodynamic states: (i) how do fast kinetics and high current in an operating electrochemical cell affect the thermodynamic states of its material constituents, (ii) whether or not the state of non-equilibrium can remain stable with constant flow of matter and energy, and (iii) what is the origin that governs activity and stability in solid oxide cells?
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7

Mazur, P. "Fluctuations and non-equilibrium thermodynamics." Physica A: Statistical Mechanics and its Applications 261, no. 3-4 (December 1998): 451–57. http://dx.doi.org/10.1016/s0378-4371(98)00353-7.

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8

van Zon, R., and E. G. D. Cohen. "Non-equilibrium thermodynamics and fluctuations." Physica A: Statistical Mechanics and its Applications 340, no. 1-3 (September 2004): 66–75. http://dx.doi.org/10.1016/j.physa.2004.03.078.

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9

Ptasinski, Krzysztof J. "Non-equilibrium thermodynamics for engineers." Energy 36, no. 3 (March 2011): 1836–37. http://dx.doi.org/10.1016/j.energy.2011.01.004.

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10

Maciołek, Anna, Robert Hołyst, Karol Makuch, Konrad Giżyński, and Paweł J. Żuk. "Parameters of State in the Global Thermodynamics of Binary Ideal Gas Mixtures in a Stationary Heat Flow." Entropy 25, no. 11 (October 31, 2023): 1505. http://dx.doi.org/10.3390/e25111505.

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In this paper, we formulate the first law of global thermodynamics for stationary states of the binary ideal gas mixture subjected to heat flow. We map the non-uniform system onto the uniform one and show that the internal energy U(S*,V,N1,N2,f1*,f2*) is the function of the following parameters of state: a non-equilibrium entropy S*, volume V, number of particles of the first component, N1, number of particles of the second component N2 and the renormalized degrees of freedom. The parameters f1*,f2*, N1,N2 satisfy the relation (N1/(N1+N2))f1*/f1+(N2/(N1+N2))f2*/f2=1 (f1 and f2 are the degrees of freedom for each component respectively). Thus, only 5 parameters of state describe the non-equilibrium state of the binary mixture in the heat flow. We calculate the non-equilibrium entropy S* and new thermodynamic parameters of state f1*,f2* explicitly. The latter are responsible for heat generation due to the concentration gradients. The theory reduces to equilibrium thermodynamics, when the heat flux goes to zero. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties.
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11

Mărgineanu, D. G. "Equilibrium and non-equilibrium approaches in biomembrane thermodynamics." Archives Internationales de Physiologie et de Biochimie 95, no. 3 (January 1987): 381–422. http://dx.doi.org/10.3109/13813458709075033.

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12

Maˇrgineanu, D. G. "Equilibrium and non-equilibrium approaches in biomembrane thermodynamics." Archives Internationales de Physiologie et de Biochimie 95, no. 4 (January 1987): 381–422. http://dx.doi.org/10.3109/13813458709113151.

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13

Oppenheim, Irwin. "Book Review: Equilibrium and Non-equilibrium Statistical Thermodynamics." Journal of Statistical Physics 117, no. 5-6 (December 2004): 1071–72. http://dx.doi.org/10.1007/s10955-004-5717-3.

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14

Dudeck, M., P. André, A. Kaminska, and M. Lino da Silva. "Thermodynamics equilibrium and non equilibrium of plasma flows." IOP Conference Series: Materials Science and Engineering 29 (February 27, 2012): 012005. http://dx.doi.org/10.1088/1757-899x/29/1/012005.

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15

Zhang, Kuan-Meng, and Yi-Xin Chen. "Non-equilibrium thermodynamics of quantum bipartite system." Modern Physics Letters B 35, no. 17 (April 15, 2021): 2150294. http://dx.doi.org/10.1142/s0217984921502948.

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In quantum information and quantum computation, a bipartite system provides a basic few-body framework for investigating significant properties of thermodynamics and statistical mechanics. A Hamiltonian model for a bipartite system is introduced to analyze the important role of interaction between bipartite subsystems in quantum non-equilibrium thermodynamics. We illustrate discrimination between such quantum thermodynamics and classical few-body non-equilibrium thermodynamics. By proposing a detailed balance condition of the bipartite system, we generally investigate the properties of the entropy and heat of our model, as well as the relation between them.
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16

Kleidon, Axel. "Non-equilibrium thermodynamics, maximum entropy production and Earth-system evolution." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1910 (January 13, 2010): 181–96. http://dx.doi.org/10.1098/rsta.2009.0188.

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The present-day atmosphere is in a unique state far from thermodynamic equilibrium. This uniqueness is for instance reflected in the high concentration of molecular oxygen and the low relative humidity in the atmosphere. Given that the concentration of atmospheric oxygen has likely increased throughout Earth-system history, we can ask whether this trend can be generalized to a trend of Earth-system evolution that is directed away from thermodynamic equilibrium, why we would expect such a trend to take place and what it would imply for Earth-system evolution as a whole. The justification for such a trend could be found in the proposed general principle of maximum entropy production (MEP), which states that non-equilibrium thermodynamic systems maintain steady states at which entropy production is maximized. Here, I justify and demonstrate this application of MEP to the Earth at the planetary scale. I first describe the non-equilibrium thermodynamic nature of Earth-system processes and distinguish processes that drive the system’s state away from equilibrium from those that are directed towards equilibrium. I formulate the interactions among these processes from a thermodynamic perspective and then connect them to a holistic view of the planetary thermodynamic state of the Earth system. In conclusion, non-equilibrium thermodynamics and MEP have the potential to provide a simple and holistic theory of Earth-system functioning. This theory can be used to derive overall evolutionary trends of the Earth’s past, identify the role that life plays in driving thermodynamic states far from equilibrium, identify habitability in other planetary environments and evaluate human impacts on Earth-system functioning.
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17

Torabi, Mohsen, Nader Karimi, Mostafa Ghiaasiaan, and Somchai Wongwises. "Non-Equilibrium Thermodynamics of Micro Technologies." Entropy 21, no. 5 (May 17, 2019): 501. http://dx.doi.org/10.3390/e21050501.

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18

Meszéna, Géza, and Hans V. Westerhoff. "Non-equilibrium thermodynamics of light absorption." Journal of Physics A: Mathematical and General 32, no. 2 (January 1, 1999): 301–11. http://dx.doi.org/10.1088/0305-4470/32/2/006.

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19

Attard, Phil. "Thermodynamics for non-equilibrium pattern formation." AIP Advances 1, no. 3 (September 2011): 032146. http://dx.doi.org/10.1063/1.3632033.

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20

Rubı́, J. M., and A. Pérez-Madrid. "Inertial effects in non-equilibrium thermodynamics." Physica A: Statistical Mechanics and its Applications 264, no. 3-4 (March 1999): 492–502. http://dx.doi.org/10.1016/s0378-4371(98)00476-2.

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21

Jou, D., G. Lebon, M. S. Mongiovı̀, and R. A. Peruzza. "Entropy flux in non-equilibrium thermodynamics." Physica A: Statistical Mechanics and its Applications 338, no. 3-4 (July 2004): 445–57. http://dx.doi.org/10.1016/j.physa.2004.02.011.

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22

Vedral, Vlatko. "Entanglement production in non-equilibrium thermodynamics." Journal of Physics: Conference Series 143 (January 7, 2009): 012010. http://dx.doi.org/10.1088/1742-6596/143/1/012010.

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23

Peppin, Stephen S. L., and Janet A. W. Elliott. "Non-equilibrium thermodynamics of concentration polarization." Advances in Colloid and Interface Science 92, no. 1-3 (September 2001): 1–72. http://dx.doi.org/10.1016/s0001-8686(00)00029-4.

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24

Yantovsky, E. I. "Non-equilibrium thermodynamics in thermal engineering." Energy 14, no. 7 (July 1989): 393–96. http://dx.doi.org/10.1016/0360-5442(89)90134-5.

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25

Callies, U., and F. Herbert. "Radiative processes and non-equilibrium thermodynamics." ZAMP Zeitschrift f�r angewandte Mathematik und Physik 39, no. 2 (March 1988): 242–66. http://dx.doi.org/10.1007/bf00945769.

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26

Al-Nimr, Moh'd Ahmad. "Non-equilibrium thermodynamics of heterogeneous systems." Energy 35, no. 5 (May 2010): 2348–49. http://dx.doi.org/10.1016/j.energy.2010.02.001.

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27

Kjelstrup, Signe, and William M. Haynes. "Expanded Focus on Non-equilibrium Thermodynamics." International Journal of Thermophysics 34, no. 7 (July 2013): 1167–68. http://dx.doi.org/10.1007/s10765-013-1489-9.

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28

Freidel, Laurent, and Yuki Yokokura. "Non-equilibrium thermodynamics of gravitational screens." Classical and Quantum Gravity 32, no. 21 (October 1, 2015): 215002. http://dx.doi.org/10.1088/0264-9381/32/21/215002.

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29

Compte, Albert, and David Jou. "Non-equilibrium thermodynamics and anomalous diffusion." Journal of Physics A: Mathematical and General 29, no. 15 (August 7, 1996): 4321–29. http://dx.doi.org/10.1088/0305-4470/29/15/007.

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30

Chirco, G., and S. Liberati. "Dissipation in non-equilibrium spacetime thermodynamics." Journal of Physics: Conference Series 222 (April 1, 2010): 012013. http://dx.doi.org/10.1088/1742-6596/222/1/012013.

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31

Dewey, T. Gregory, and Mariano Delle Donne. "Non-equilibrium Thermodynamics of Molecular Evolution." Journal of Theoretical Biology 193, no. 4 (August 1998): 593–99. http://dx.doi.org/10.1006/jtbi.1998.0724.

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32

Entov, Michael, and Leonid Polterovich. "Contact topology and non-equilibrium thermodynamics." Nonlinearity 36, no. 6 (May 17, 2023): 3349–75. http://dx.doi.org/10.1088/1361-6544/acd1ce.

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Abstract We describe a method, based on contact topology, of showing the existence of semi-infinite trajectories of contact Hamiltonian flows which start on one Legendrian submanifold and asymptotically converge to another Legendrian submanifold. We discuss a mathematical model of non-equilibrium thermodynamics where such trajectories play a role of relaxation processes, and illustrate our results in the case of the Glauber dynamics for the mean field Ising model.
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33

Kovács, Róbert, Patrizia Rogolino, and Francesco Oliveri. "Mathematical Aspects in Non-Equilibrium Thermodynamics." Symmetry 15, no. 4 (April 17, 2023): 929. http://dx.doi.org/10.3390/sym15040929.

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34

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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35

Fukuda, R. "Non-Equilibrium Thermodynamics and Its Corrections to Thermal Equilibrium." Progress of Theoretical Physics 77, no. 4 (April 1, 1987): 825–44. http://dx.doi.org/10.1143/ptp.77.825.

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36

Siginc, Onur, Mustafa Salti, Hilmi Yanar, and Oktay Aydogdu. "Cosmology in scalar–tensor–vector theory via thermodynamics." Modern Physics Letters A 33, no. 24 (August 3, 2018): 1850137. http://dx.doi.org/10.1142/s0217732318501377.

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Assuming the universe as a thermodynamical system, the second law of thermodynamics can be extended to another form including the sum of matter and horizon entropies, which is called the generalized second law of thermodynamics. The generalized form of the second law (GSL) is universal which means it holds both in non-equilibrium and equilibrium pictures of thermodynamics. Considering the universe is bounded by a dynamical apparent horizon, we investigate the nature of entropy function for the validity of GSL in the scalar–tensor–vector (STEVE) theory of gravity.
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37

Nakagawa, Naoko, and Shin-ichi Sasa. "Global Thermodynamics for Heat Conduction Systems." Journal of Statistical Physics 177, no. 5 (October 8, 2019): 825–88. http://dx.doi.org/10.1007/s10955-019-02393-2.

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Abstract We propose the concept of global temperature for spatially non-uniform heat conduction systems. With this novel quantity, we present an extended framework of thermodynamics for the whole system such that the fundamental relation of thermodynamics holds, which we call “global thermodynamics” for heat conduction systems. Associated with this global thermodynamics, we formulate a variational principle for determining thermodynamic properties of the liquid-gas phase coexistence in heat conduction, which corresponds to the natural extension of the Maxwell construction for equilibrium systems. We quantitatively predict that the temperature of the liquid–gas interface deviates from the equilibrium transition temperature. This result indicates that a super-cooled gas stably appears near the interface.
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38

Borlenghi, Simone, and Anna Delin. "Stochastic Thermodynamics of Oscillators’ Networks." Entropy 20, no. 12 (December 19, 2018): 992. http://dx.doi.org/10.3390/e20120992.

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We apply the stochastic thermodynamics formalism to describe the dynamics of systems of complex Langevin and Fokker-Planck equations. We provide in particular a simple and general recipe to calculate thermodynamical currents, dissipated and propagating heat for networks of nonlinear oscillators. By using the Hodge decomposition of thermodynamical forces and fluxes, we derive a formula for entropy production that generalises the notion of non-potential forces and makes transparent the breaking of detailed balance and of time reversal symmetry for states arbitrarily far from equilibrium. Our formalism is then applied to describe the off-equilibrium thermodynamics of a few examples, notably a continuum ferromagnet, a network of classical spin-oscillators and the Frenkel-Kontorova model of nano friction.
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39

Pekař, Miloslav. "Thermodynamic Analysis of the Landolt-Type Autocatalytic System." Catalysts 11, no. 11 (October 28, 2021): 1300. http://dx.doi.org/10.3390/catal11111300.

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A recent work demonstrated the example of the Landolt-type reaction system and how the simplest autocatalytic loop is described by the kinetic mass action law and proper parametrization of direct and autocatalytic pathways. Using a methodology of non-equilibrium thermodynamics, the thermodynamic consistency of that kinetic model is analyzed and the mass action description is generalized, including an alternative description by the empirical rate equation. Relationships between independent and dependent reactions and their rates are given. The mathematical modeling shows that following the time evolution of reaction rates provides additional insight into autocatalytic behavior. A brief note on thermodynamic driving forces and coupling with diffusion is added. In summary, this work extends and generalizes the kinetic description of the Landolt-type system, placing it within the framework of non-equilibrium thermodynamics and demonstrating its thermodynamic consistency.
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40

Nettleton, R. E. "Scalar Fluctuations from Extended Non-equilibrium Thermodynamic States." Zeitschrift für Naturforschung A 40, no. 10 (October 1, 1985): 976–85. http://dx.doi.org/10.1515/zna-1985-1003.

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In the framework of extended non-equilibrium thermodynamics, the local non-equilibrium state of a liquid is described by the density, temperature, and a structural variable, ζ, and its rate-of-change. ζ is the ensemble average of a function A (Q) of the configuration co-ordinates, and it is assumed to relax to local equilibrium in a time short compared to the time for diffusion of an appreciable number of particles into the system. By a projection operator technique of Grabert, an equation is derived from the Liouville equation for the distribution of fluctuations in TV, the particle number, and in A and Ȧ. An approximate solution is proposed which exhibits nonequilibrium corrections to the Einstein function in the form of a sum of thermodynamic forces. For a particular structural model, the corresponding non-Einstein contributions to correlation functions are estimated to be very small. For variables of the type considered here, the thermodynamic pressure is found to equal the pressure trace.
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41

Szücs, Mátyás, and Tamás Fülöp. "Kluitenberg–Verhás Rheology of Solids in the GENERIC Framework." Journal of Non-Equilibrium Thermodynamics 44, no. 3 (July 26, 2019): 247–59. http://dx.doi.org/10.1515/jnet-2018-0074.

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Abstract The internal variable methodology of non-equilibrium thermodynamics, with a symmetric tensorial internal variable, provides an important rheological model family for solids, the so-called Kluitenberg–Verhás model family [Cs. Asszonyi et al., Contin. Mech. Thermodyn. 27, 2015]. This model family is distinguished not only by theoretical aspects but also on experimental grounds (see [Cs. Asszonyi et al., Period. Polytech., Civ. Eng. 60, 2016] for plastics and [W. Lin et al., Rock Engineering in Difficult Ground Conditions (Soft Rock and Karst), Proceedings of Eurock’09, 2009; K. Matsuki, K. Takeuchi, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 30, 1993; K. Matsuki, Int. J. Rock Mech. Min. Sci. 45, 2008] for rocks). In this article, we present and discuss how the internal variable formulation of the Kluitenberg–Verhás model family can be presented in the non-equilibrium thermodynamical framework GENERIC (General Equation for the Non-Equilibrium Reversible–Irreversible Coupling) [H. C. Öttinger, Beyond Equilibrium Thermodynamics, 2005; M. Grmela, J. Non-Newton. Fluid Mech. 165, 2010; M. Grmela, H. C. Öttinger, Phys. Rev. E 56, 1997; H. C. Öttinger, M. Grmela, Phys. Rev. E 56, 1997], for the benefit of both thermodynamical methodologies and promising practical applications.
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42

Fukuda, R. "Non-Equilibrium Thermodynamics and Its Corrections to Thermal Equilibrium. II." Progress of Theoretical Physics 77, no. 4 (April 1, 1987): 845–63. http://dx.doi.org/10.1143/ptp.77.845.

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43

Shimoji, Mitsuo, and Toshio Itami. "1.1 Phenomenological Law and Non-Equilibrium Thermodynamics." Defect and Diffusion Forum 43 (January 1986): 2–14. http://dx.doi.org/10.4028/www.scientific.net/ddf.43.2.

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44

García-March, Miguel Ángel, Thomás Fogarty, Steve Campbell, Thomas Busch, and Mauro Paternostro. "Non-equilibrium thermodynamics of harmonically trapped bosons." New Journal of Physics 18, no. 10 (October 21, 2016): 103035. http://dx.doi.org/10.1088/1367-2630/18/10/103035.

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45

Santamaría-Holek, I., J. M. Rubí, and A. Pérez-Madrid. "Mesoscopic thermodynamics of stationary non-equilibrium states." New Journal of Physics 7 (February 1, 2005): 35. http://dx.doi.org/10.1088/1367-2630/7/1/035.

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46

Garden, J. L. "Macroscopic non-equilibrium thermodynamics in dynamic calorimetry." Thermochimica Acta 452, no. 2 (January 2007): 85–105. http://dx.doi.org/10.1016/j.tca.2006.08.017.

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47

Sengupta, Tapan K., Aditi Sengupta, K. S. Shruti, Soumyo Sengupta, and Ashish Bhole. "Non-equilibrium Thermodynamics of Rayleigh-Taylor instability." Journal of Physics: Conference Series 759 (October 2016): 012079. http://dx.doi.org/10.1088/1742-6596/759/1/012079.

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Bedeaux, D., and P. Mazur. "Mesoscopic non-equilibrium thermodynamics for quantum systems." Physica A: Statistical Mechanics and its Applications 298, no. 1-2 (September 2001): 81–100. http://dx.doi.org/10.1016/s0378-4371(01)00223-0.

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Lucia, Umberto. "Considerations on non equilibrium thermodynamics of interactions." Physica A: Statistical Mechanics and its Applications 447 (April 2016): 314–19. http://dx.doi.org/10.1016/j.physa.2015.12.063.

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Rubi, J. Miguel. "Non-equilibrium thermodynamics of small-scale systems." Energy 32, no. 4 (April 2007): 297–300. http://dx.doi.org/10.1016/j.energy.2005.11.013.

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