Steady-state entropy: a proposal based on thermodynamic integration
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Universidade Federal de Minas Gerais
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Artigo de periódico
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Defining an entropy function out of equilibrium is an outstanding challenge. For stochastic lattice models in spatially uniform nonequilibrium steady states, definitions of temperature T and chemical potential μ have been verified using coexistence with heat and particle reservoirs. For an appropriate choice of exchange rates, T and
μ satisfy the zeroth law, marking an important step in the development of steady-state thermodynamics. These results suggest that an associated steady-state entropy Sth be constructed via thermodynamic integration, using
relations such as (∂S/∂E)V,N = 1/T , ensuring that derivatives of Sth with respect to energy and particle number yield the expected intensive parameters. We determine via direct calculation the stationary nonequilibrium probability distribution of the driven lattice gas with nearest-neighbor exclusion, the Katz-Lebowitz-Spohn
driven lattice gas, and a two-temperature Ising model so that we may evaluate the Shannon entropy SS as well
as Sth defined above. Although the two entropies are identical in equilibrium (as expected), they differ out of equilibrium; for small values of the drive, D, we find |SS − Sth| ∝ D2, as expected on the basis of symmetry.
We verify that Sth is not a state function: changes Sth depend not only on the initial and final points, but also on the path in parameter space. The inequivalence of SS and Sth implies that derivatives of SS are not predictive of coexistence. In other words, a nonequilibrium steady state is not determined by maximizing the Shannon entropy. Our results cast doubt on the possibility of defining a state function that plays the role of a thermodynamic entropy for nonequilibrium steady states.
Abstract
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Termodinâmica, Gás de rede, Entropia
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Thermodynamics, Sistemas fora de equilíbrio, Gás de rede dirigido, Entropy
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https://journals.aps.org/pre/abstract/10.1103/PhysRevE.99.032137