# The stochastic motion of self-thermophoretic Janus particles

## TL;DR

This paper develops Langevin equations for self-thermophoretic Janus particles, linking stochastic hydrodynamics and heat transfer to describe their motion and energy transfer under nonequilibrium conditions.

## Contribution

It introduces a comprehensive stochastic framework for Janus particle dynamics, incorporating radiative heat transfer and boundary conditions, advancing understanding of their nonequilibrium behavior.

## Key findings

- Derived Langevin equations for particle motion and heat transfer.
- Established fluctuation relations connecting displacement and energy transfer.
- Provided expressions for self-thermophoretic velocity and reciprocal effects.

## Abstract

Langevin equations for the self-thermophoretic dynamics of Janus motors partially coated with an absorbing layer that is heated by a radiation field are presented. The derivation of these equations is based on fluctuating hydrodynamics and radiative heat transfer theory involving stochastic equations for bulk phases and surface processes that are consistent with microscopic reversibility. Expressions for the self-thermophoretic force and torque for arbitrary slip boundary conditions are obtained. The overdamped Langevin equations for the colloid displacement and radiative heat transfer provide expressions for the self-thermophoretic velocity and its reciprocal contribution where an external force can influence the radiative heat transfer. A nonequilibrium fluctuation formula is also derived and shows how the probability density of the Janus particle displacement and radiation energy transfer during the time interval [0,t] are related to the mechanical and thermal affinities that characterize the nonequilibrium system state.