Energy distribution and effective temperatures in a driven dissipative model

TL;DR

This paper analyzes the non-equilibrium energy distribution and various effective temperatures in a driven dissipative system, revealing differences among temperature measures and characterizing the system's steady state.

Contribution

It provides an exact solution for the steady state energy distribution and explores multiple definitions of effective temperature in a non-equilibrium context.

Findings

Energy distribution tail is exponential.

Different effective temperature measures generally do not coincide.

Relations between various temperature definitions are established.

Abstract

We investigate non-equilibrium behavior of driven dissipative systems, using the model presented in [Phys. Rev. Lett. 93, 240601 (2004)]. We solve the non-Boltzmann steady state energy distribution and the temporal evolution to it, and find its high energy tail to behave exponentially. We demonstrate that various measures of effective temperatures generally differ. We discuss infinite hierarchies of effective temperatures defined from moments of the non-exponential energy distribution, and relate them to the "configurational temperature", measured directly from instantaneous particle locations without any kinetic information. We calculate the "granular temperature", characterizing the average energy in the system, two different "fluctuation temperatures", scaling fluctuation-dissipation relations, and the "entropic temperature", defined from differentiating the entropy with respect to energy.