Extended Heat-Fluctuation Theorems for a System with Deterministic and Stochastic Forces

TL;DR

This paper derives extended heat-fluctuation theorems for a Brownian particle influenced by deterministic and stochastic forces, revealing significant deviations from conventional theorems especially for large heat fluctuations.

Contribution

It provides exact Fourier transforms and analytical results for heat fluctuation distributions in a system with combined deterministic and stochastic dynamics, extending traditional fluctuation theorems.

Findings

Extended fluctuation theorem differs from the conventional one.

Large heat fluctuations show a much higher probability of heat absorption.

Analytical results agree well with numerical simulations for moderate times.

Abstract

Heat fluctuations over a time \tau in a non-equilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components: a Brownian particle dragged through a fluid by a harmonic potential which is moved with constant velocity. Using a Langevin equation, we find the exact Fourier transform of the distribution of these fluctuations for all \tau. By a saddle-point method we obtain analytical results for the inverse Fourier transform, which, for not too small \tau, agree very well with numerical results from a sampling method as well as from the fast Fourier transform algorithm. Due to the interaction of the deterministic part of the motion of the particle in the mechanical potential with the stochastic part of the motion caused by the fluid, the conventional heat fluctuation theorem is, for infinite and for finite \tau, replaced by an extended fluctuation theorem that differs noticeably and measurably from it. In particular, for large fluctuations, the ratio of the probability for absorption of heat (by the particle from the fluid) to the probability to supply heat (by the particle to the fluid) is much larger here than in the conventional fluctuation theorem.