The Fluctuation Theorem and Green-Kubo Relations

TL;DR

This paper derives transport coefficients for fluids in nonequilibrium steady states using the Fluctuation Theorem and Gaussian assumptions, confirming their validity in the linear regime but not in nonlinear, far-from-equilibrium conditions.

Contribution

It connects the Fluctuation Theorem with Green-Kubo relations and clarifies their applicability limits to linear response regimes.

Findings

Green-Kubo expressions are valid in the linear regime

Derived transport coefficients align with linear response theory

Expressions break down in nonlinear, far-from-equilibrium conditions

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.