Stochastic thermodynamics of Brownian motion in a flowing fluid

TL;DR

This paper develops a stochastic thermodynamics framework for Brownian particles in flowing fluids, treating flow as a non-conservative force, and verifies the second law and fluctuation theorems through simulations.

Contribution

It introduces a novel approach to analyze thermodynamics of Brownian motion in flow fields as non-conservative forces, extending existing theories.

Findings

Second law of thermodynamics is explicitly proven.

Fluctuation theorems are derived and verified.

Comparison with previous theories highlights new insights.

Abstract

We study stochastic thermodynamics of over-damped Brownian motion in a flowing fluid. Unlike some previous works, we treat the effects of the flow field as a non-conservational driving force acting on the Brownian particle. This allows us to apply the theoretical formalism developed in a recent work for general non-conservative Langevin dynamics. We define heat and work both at the trajectory level and at the ensemble level, and prove the second law of thermodynamics explicitly. The entropy production (EP) is decomposed into a housekeeping part and an excess part, both of which are non-negative at the ensemble level. Fluctuation theorems are derived for the housekeeping work, the excess work, and the total work, which are further verified using numerical simulations. A comparison between our theory and an earlier theory by Speck et. al. is also carried out.