Fluctuation Theorem, non linear response and the regularity of time reversal symmetry

TL;DR

This paper explores the Gallavotti-Cohen Fluctuation Theorem's implications for nonlinear response and time reversal symmetry, showing that non-differentiability can violate the theorem, with comparisons to Lebowitz-Spohn FT.

Contribution

It demonstrates how non-differentiability of time reversal symmetry affects the validity of the Gallavotti-Cohen FT in a simple reversible system.

Findings

Violation of FT due to non-differentiability of time reversal symmetry

Derivation of identities generalizing Green-Kubo formula to nonlinear regime

Comparison between Gallavotti-Cohen and Lebowitz-Spohn fluctuation theorems

Abstract

The Gallavotti - Cohen Fluctuation Theorem (FT) implies an infinite set of identities between correlation functions that can be seen as a generalization of Green Kubo formula to the nonlinear regime. As an application, we discuss a perturbative check of the FT relation through these identities for a simple Anosov reversible system; we find that the lack of differentiability of the time reversal symmetry implies a violation of the Gallavotti - Cohen fluctuation relation. Finally, a brief comparison with Lebowitz - Spohn FT is reported.