Heat Dissipation from Brownian Particles under Hydrodynamic Interactions

TL;DR

This paper investigates the non-equilibrium thermodynamics of Brownian macromolecules with hydrodynamic interactions and feedback control, deriving heat, work, and entropy production with a focus on stochastic integration and physical consistency.

Contribution

It introduces a framework for analyzing thermodynamic quantities of Brownian particles with hydrodynamic interactions and feedback, emphasizing the importance of the Stratonovich prescription for stochastic integration.

Findings

Stratonovich integration is the unique physical choice for heat calculation.

Thermodynamic quantities are unambiguous when diffusion matrix and feedback are known.

The approach clarifies the role of hydrodynamic interactions in non-equilibrium thermodynamics.

Abstract

We study the non-equilibrium thermodynamics of single Brownian macromolecules immersed in water solvent. They are under both a hydrodynamic interaction and a feedback control on their movement by an external agent. The macromolecules are described by a Langevin equation with a multiplicative noise. Work done by the macromolecules on the water solvent is dissipated as heat. Thus, the heat is expressed as the integration of an interacting force between the macromolecules and the water solvent along the position space trajectories of the macromolecules. This integration is stochastic due to the Brownian motion of the macromolecules. We show that the Stratonovich prescription of the integration is the unique physical choice. We also show that thermodynamic quantities such as heat, work, and entropy production, are derived without any ambiguity if both a diffusion matrix and external feedback control are known as priori.