Overdamped stochastic thermodynamics with multiple reservoirs

TL;DR

This paper develops a stochastic thermodynamics framework for overdamped Langevin systems with multiple reservoirs, highlighting differences from naive models and deriving heat statistics for a specific system.

Contribution

It introduces a correct overdamped theory for systems with multiple reservoirs, accounting for nonequilibrium momentum dynamics, and derives analytical heat statistics.

Findings

Overdamped theory differs from naive models in multiple-reservoir systems.

Both theories satisfy fluctuation theorems.

Heat statistics agree in the long-time limit for the studied system.

Abstract

After establishing stochastic thermodynamics for underdamped Langevin systems in contact with multiple reservoirs, we derive its overdamped limit using timescale separation techniques. The overdamped theory is different from the naive theory that one obtains when starting from overdamped Langevin or Fokker-Planck dynamics and only coincide with it in presence of a single reservoir. The reason is that the coarse-grained fast momenta dynamics reaches a nonequilibrium state which conducts heat in presence of multiple reservoirs. The underdamped and overdamped theory are both shown to satisfy fundamental fluctuation theorems. Their predictions for the heat statistics are derived analytically for a Brownian particle on a ring in contact with two reservoirs and subjected to a non-conservative force and are shown to coincide in the long-time limit.