Generalised Einstein Relation for Hot Brownian Motion

TL;DR

This paper develops a generalized Einstein relation for hot Brownian motion, validated through molecular dynamics simulations, linking effective temperature to measurable quantities in nanoparticle systems.

Contribution

It introduces a formally exact theoretical prediction and a generalized Einstein relation for hot Brownian motion, supported by simulation data.

Findings

Effective temperatures $T_{HBM}$ and $T_k$ are Boltzmann distributed.

Derived a generalized Einstein relation connecting $T_{HBM}$ to measurable parameters.

Simulation results confirm theoretical predictions across a wide temperature range.

Abstract

The Brownian motion of a hot nanoparticle is described by an effective Markov theory based on fluctuating hydrodynamics. Its predictions are scrutinized over a wide temperature range using large-scale molecular dynamics simulations of a hot nanoparticle in a Lennard-Jones fluid. The particle positions and momenta are found to be Boltzmann distributed according to distinct effective temperatures $T_\mathrm{HBM}$ and $T_\mathrm{k}$ . For $T_\mathrm{HBM}$ we derive a formally exact theoretical prediction and establish a generalised Einstein relation that links it to directly measurable quantities.