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Zwanzig, J. Mori, Progr. Balian, Y. Alhassid, and H. Reinhardt, Phys. Personalised recommendations.

Thermodynamics Equilibrium- Chemical, Mechanical and Thermal Equilibrium-

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The article on Onsager reciprocal relations considers the stable near-steady thermodynamically non-equilibrium regime, which has dynamics linear in the forces and flux densities. In stationary conditions, such forces and associated flux densities are by definition time invariant, as also are the system's locally defined entropy and rate of entropy production. Notably, according to Ilya Prigogine and others, when an open system is in conditions that allow it to reach a stable stationary thermodynamically non-equilibrium state, it organizes itself so as to minimize total entropy production defined locally.

This is considered further below. One wants to take the analysis to the further stage of describing the behaviour of surface and volume integrals of non-stationary local quantities; these integrals are macroscopic fluxes and production rates. In general the dynamics of these integrals are not adequately described by linear equations, though in special cases they can be so described. This fact is called the Onsager reciprocal relations.

The generalization of the above equations for the rate of creation of entropy was given by Pokrovskii. Until recently, prospects for useful extremal principles in this area have seemed clouded. Nicolis [47] concludes that one model of atmospheric dynamics has an attractor which is not a regime of maximum or minimum dissipation; she says this seems to rule out the existence of a global organizing principle, and comments that this is to some extent disappointing; she also points to the difficulty of finding a thermodynamically consistent form of entropy production.

Another top expert offers an extensive discussion of the possibilities for principles of extrema of entropy production and of dissipation of energy: Chapter 12 of Grandy [2] is very cautious, and finds difficulty in defining the 'rate of internal entropy production' in many cases, and finds that sometimes for the prediction of the course of a process, an extremum of the quantity called the rate of dissipation of energy may be more useful than that of the rate of entropy production; this quantity appeared in Onsager's [10] origination of this subject. Other writers have also felt that prospects for general global extremal principles are clouded.

A recent proposal may perhaps by-pass those clouded prospects. It is also used to give a description of the dynamics of nanoparticles, which can be out of equilibrium in systems where catalysis and electrochemical conversion is involved.

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Nonequilibrium Thermodynamics

Classical Statistical Chemical Quantum thermodynamics. Zeroth First Second Third. System properties. Note: Conjugate variables in italics. Work Heat. Material properties. Carnot's theorem Clausius theorem Fundamental relation Ideal gas law. Free energy Free entropy. History Culture.

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History General Entropy Gas laws. Entropy and time Entropy and life Brownian ratchet Maxwell's demon Heat death paradox Loschmidt's paradox Synergetics. Caloric theory Theory of heat. Heat ". Thermodynamics Heat engines. Main article: Onsager reciprocal relations. Main article: Extremal principles in non-equilibrium thermodynamics.

Non-Equilibrium Thermodynamics

Physica D: Nonlinear Phenomena. Proceedings of the London Mathematical Society. Physical Review. Bibcode : PhRv Entropy transfer and production". Astrophysical Journal. Bibcode : ApJ Journal of the Atmospheric Sciences. Bibcode : JAtS Planetary and Space Science. Non-equilibrium Thermodynamics , North-Holland, Amsterdam. Probability and Heat: Fundamentals of Thermostatistics , Freidr. Bibcode : ArRMA..

Modern Thermodynamics.

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Nonequilibrium Statistical Thermodynamics , translated from the Russian by P. Shepherd, New York, Consultants Bureau. Monthly Notices of the Royal Astronomical Society. Equations of Motion". Foundations of Physics. Bibcode : FoPh The Entropy". III: Selected Applications". Rational Thermodynamics 2 ed. Continuum Thermomechanics. The Mechanics and Thermodynamics of Continua. Cambridge University Press. Thermodynamics of Materials with Memory: Theory and Applications.

Non-equilibrium thermodynamics as a tool to compute temperature at the catalyst surface

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Nonequilibrium Thermodynamics - 4th Edition

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