Generalized fluctuation theorems for classical systems

TL;DR

This paper derives generalized fluctuation theorems for classical Gaussian Markov processes, including non-trivial systems like an electron in a magnetic field, extending their applicability to non-equilibrium steady states.

Contribution

It provides a general form of fluctuation theorems for Gaussian Markov processes and identifies conditions for the universal parameter 1/kT.

Findings

Derived the general fluctuation theorem form for Gaussian Markov processes.

Identified conditions under which the parameter becomes universal 1/kT.

Applied the generalized theorem to classical cyclotron motion of an electron.

Abstract

Fluctuation theorems have a very special place in the study of non equilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen Fluctuation Theorem which is in terms of the distribution of the work $p(W)/p(-W)=\exp(\alpha W)$. We derive the general form of the fluctuation theorems for an arbitrary Gaussian Markov process and find conditions when the parameter $\alpha$ becomes a universal parameter $1/kT$. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is non-trivial. The generalized theorems are equally valid for non-equilibrium steady states.