Non-Isothermal Fluctuation-Dissipation Relations and Brownian Thermometry

TL;DR

This paper extends the classical fluctuation-dissipation relations to non-isothermal conditions, deriving generalized Langevin equations and analyzing Brownian thermometry far from equilibrium.

Contribution

It introduces a generalized fluctuation-dissipation framework applicable to non-isothermal Brownian motion, including explicit frequency-dependent noise temperature results.

Findings

Derived generalized fluctuation-dissipation relations for non-isothermal systems

Formulated Langevin equations for non-isothermal Brownian motion

Provided explicit results for frequency-dependent noise temperature

Abstract

The classical theory of Brownian motion rests on fundamental laws of statistical mechanics, such as the equipartition theorem and the fluctuation-dissipation theorem, which are not applicable in non-isothermal situations. We derive the generalized fluctuation-dissipation relations and Langevin equations governing such non-isothermal Brownian motion, including explicit results for the frequency-dependent noise temperature and Brownian thermometry far from equilibrium.