Effective temperatures of a heated Brownian particle

TL;DR

This paper explores different definitions of effective temperature for a heated Brownian particle, revealing their dependence on time scales and consistency with kinetic and fluctuation theorem-based temperatures.

Contribution

It compares various effective temperature definitions in a nonequilibrium system and clarifies their relationships and limitations.

Findings

Effective temperature depends on the time scale considered.

Short and long time limits of the effective temperature align with kinetic energy and Einstein relation.

Fluctuation theorem temperature matches the short time fluctuation dissipation ratio.

Abstract

We investigate various possible definitions of an effective temperature for a particularly simple nonequilibrium stationary system, namely a heated Brownian particle suspended in a fluid. The effective temperature based on the fluctuation dissipation ratio depends on the time scale under consideration, so that a simple Langevin description of the heated particle is impossible. The short and long time limits of this effective temperature are shown to be consistent with the temperatures estimated from the kinetic energy and Einstein relation, respectively. The fluctuation theorem provides still another definition of the temperature, which is shown to coincide with the short time value of the fluctuation dissipation ratio.