Effective Langevin equations leading to large deviation function of time-averaged velocity for a nonequilibrium Rayleigh piston

TL;DR

This paper derives effective Langevin equations to accurately describe the large deviation function of the time-averaged velocity of a piston in a nonequilibrium gas system, providing insights into its fluctuating dynamics.

Contribution

It introduces a method to construct infinite effective Langevin equations that reproduce the large deviation function of the piston’s velocity in a nonequilibrium setting.

Findings

Derived the large deviation function for the piston velocity.

Constructed an infinite set of effective Langevin equations.

Proposed methods to uniquely determine the effective model form.

Abstract

We study fluctuating dynamics of a freely movable piston that separates an infinite cylinder into two regions filled with ideal gas particles at the same pressure but different temperatures. To investigate statistical properties of the time-averaged velocity of the piston in the long-time limit, we perturbatively calculate the large deviation function of the time-averaged velocity. Then, we derive an infinite number of effective Langevin equations yielding the same large deviation function as in the original model. Finally, we provide two possibilities for uniquely determining the form of the effective model.