Stochastic Thermodynamics of Brownian motion in Temperature Gradient

TL;DR

This paper develops a stochastic thermodynamics framework for Brownian particles in temperature gradients, deriving fluctuation theorems and verifying them through molecular dynamics simulations, including under-damped regimes.

Contribution

It formulates an experimentally accessible over-damped Langevin theory for particles in temperature gradients and demonstrates the validity of fluctuation theorems even in under-damped conditions.

Findings

Fluctuation theorem remains valid in under-damped regime.

Derived Clausius inequality for non-uniform temperature environments.

Verified fluctuation theorem via molecular dynamics simulations.

Abstract

We study stochastic thermodynamics of a Brownian particle which is subjected to a temperature gradient and is confined by an external potential. We first formulate an over-damped Ito-Langevin theory in terms of local temperature, friction coefficient, and steady state distribution, all of which are experimentally measurable. We then study the associated stochastic thermodynamics theory. We analyze the excess entropy production (EP) both at trajectory level and at ensemble level, and derive the Clausius inequality as well as the transient fluctuation theorem (FT). We also use molecular dynamics to simulate a Brownian particle inside a Lennard-Jones fluid and verify the FT. Remarkably we find that the FT remains valid even in the under-damped regime. We explain the possible mechanism underlying this surprising result.