The Fluctuation Theorem and Green-Kubo Relations

Abstract

Green-Kubo and Einstein expressions for the transport coefficients of a fluid in a nonequilibrium steady state can be derived using the Fluctuation Theorem and by assuming the probability distribution of the time-averaged dissipative flux is Gaussian. These expressions are consistent with those obtained using linear response theory and are valid in the linear regime. It is shown that these expressions are however, not valid in the nonlinear regime where the fluid is driven far from equilibrium. We advance an argument for why these expression are only valid in the linear response, zero field limit.

32 pages, inc. 6 figures Discussion and notation improved

References in corpus (6)

• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• The Fluctuation Theorem as a Gibbs Property
• The Fluctuation Theorem for Stochastic Systems
• Note on Two Theorems in Nonequilibrium Statistical Mechanics
• (Global and Local) Fluctuations of Phase Space Contraction in Deterministic Stationary Non-equilibrium
• On the Asymptotic Convergence of the Transient and Steady State Fluctuation Theorems

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