On Irreversibility, Dissipation and Response Theory

TL;DR

This paper explores the role of the dissipation function in fluctuation theorems and nonlinear response theory, deriving exact relations that connect microscopic reversibility with macroscopic irreversibility and response behaviors.

Contribution

It introduces the Dissipation Theorem, providing exact nonlinear response relations for classical N-body systems, linking fluctuation theorems with response theory.

Findings

Derives the Dissipation Theorem for nonlinear response

Shows the dissipation function's central role in fluctuation theorems

Reduces to Green-Kubo relations in the linear limit

Abstract

Recently there has been considerable interest in the Fluctuation Theorem (FT). The FT shows how time reversible microscopic dynamics leads to irreversible macroscopic behavior as the system size or observation time increases. We show that the argument of the Evans-Searles FT, the dissipation function, plays a central role in nonlinear response theory and derive the Dissipation Theorem, giving exact relations for nonlinear response of classical N-body systems. These expressions should be verifiable experimentally. When linearized they reduce to the Green-Kubo expressions for linear response.