Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States

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Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States (2002)

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by L. Bertini , A. De Sole , D. Gabrielli , G. Jona-lasinio , C. Landim

Venue:	JOURNAL OF STATISTICAL PHYSICS
Citations:	78 - 13 self

BibTeX

@ARTICLE{Bertini02macroscopicfluctuation,
    author = {L. Bertini and A. De Sole and D. Gabrielli and G. Jona-lasinio and C. Landim},
    title = {Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States},
    journal = {JOURNAL OF STATISTICAL PHYSICS},
    year = {2002},
    volume = {107},
    number = {3},
    pages = {635--675}
}

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Abstract

We formulate a dynamical fluctuation theory for stationary non-equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager–Machlup theory in the SNS; a general Hamilton–Jacobi equation for the macroscopic entropy; a non-equilibrium, nonlinear fluctuation dissipation relation valid for a wide class of systems; an H theorem for the entropy. We discuss in detail two models of stochastic boundary driven lattice gases: the zero range and the simple exclusion processes. In the first model the invariant measure is explicitly known and we verify the predictions of the general theory. For the one dimensional simple exclusion process, as recently shown by Derrida, Lebowitz, and Speer, it is possible to express the macroscopic entropy in terms of the solution of a nonlinear ordinary differential equation; by using the Hamilton–Jacobi equation, we obtain a logically independent derivation of this result.

Keyphrases

stationary non-equilibrium state macroscopic fluctuation theory macroscopic entropy hamilton jacobi equation crucial role independent derivation general theory wide class stochastic model zero range stochastic boundary driven lattice gas general hamilton jacobi equation invariant measure nonlinear ordinary differential equation nonlinear fluctuation dissipation relation valid dynamical fluctuation theory onsager machlup theory following result dimensional simple exclusion process first model simple exclusion process

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