Gianmaria Falasco — Universität Leipzig #
Nonisothermal Brownian motion #
The theory of isothermal Brownian motion relies on fundamental principles of equilibrium statistical 
mechanics, such as the equipartition theorem, embedded in the stochastic framework of the Langevin 
equation. In the presence of a nonisothermal solvent it becomes questionable whether a Langevin-like 
description still applies and, if so, no general criterion exists which uniquely determines friction and 
thermal fluctuations. Starting from the fluctuating hydrodynamics of a solvent in local equilibrium, we 
constructively show that a generalized Langevin description does hold and derive the statistics of the 
corresponding thermal noise. The coupling between the hydrodynamic modes excited by the particle itself 
and the solvent temperature gradient turns the energy spectrum of the Langevin noise into a 
frequency-dependent tensor. We derive an explicit expression for this energy spectrum in the analytically 
tractable case of hot Brownian motion, i.e. a constantly heated particle generating a comoving radial 
temperature field. This allows us to explain the break of energy equipartition and to express the energy 
content of the particle velocity and position in terms of effective temperatures.