Non-isothermal fluctuating hydrodynamics and Brownian motion

TL;DR

This paper extends the classical fluctuating hydrodynamics framework to non-isothermal conditions, deriving stochastic equations for Brownian motion that account for temperature variations, with negligible effects from temperature fluctuations under typical conditions.

Contribution

It develops a non-isothermal generalization of fluctuating hydrodynamics and Brownian motion, incorporating local thermal effects into the stochastic equations of motion.

Findings

Temperature fluctuations have negligible impact on Brownian dynamics under typical conditions.

The derived equations generalize classical Brownian motion models to non-isothermal environments.

Abstract

The classical theory of Brownian dynamics follows from coarse-graining the underlying linearized fluctuating hydrodynamics of the solvent. We extend this procedure to globally non-isothermal conditions, requiring only a local thermal equilibration of the solvent. Starting from the conservation laws, we establish the stochastic equations of motion for the fluid momentum fluctuations in the presence of a suspended Brownian particle. These are then contracted to the non-isothermal generalized Langevin description of the suspended particle alone, for which the coupling to stochastic temperature fluctuations is found to be negligible under typical experimental conditions.