Relation between two proposed fluctuation theorems

TL;DR

This paper investigates the relationship between two fluctuation theorems, demonstrating that for Langevin thermostatted steady states, the heat function aligns with the phase space compression, confirming the GCFT's inapplicability in these systems.

Contribution

It shows that for Langevin thermostatted steady states, the heat function equals the phase space compression, clarifying the applicability of fluctuation theorems.

Findings

Heat function equals phase space compression in Langevin systems.

GCFT does not apply to thermostatted steady states.

Supports van Zon and Cohen's extension of fluctuation theorems.

Abstract

Recently van Zon and Cohen [1-3] proposed an extension of the Fluctuation Theorems (FTs) of Evans and Searles [4]. For dissipative nonequilibrium systems, Cohen and van Zon studied the fluctuations of the heat absorbed, over a period of time t, by a surrounding thermostat. They showed theoretically that for thermostatted systems their extension does not exhibit the standard form expected for FTs and In the present paper we show that for thermostatted nonequilibrium steady states modeled by Langevin dynamics, the heat function is in fact identical to the time integral of the phase space compression factor which appears in the Gallavotti-Cohen FT (GCFT). Thus the work of van Zon and Cohen confirms at least for Langevin systems, that the GCFT does not apply to thermostatted steady states.