Dependence of the fluctuation-dissipation temperature on the choice of observable

TL;DR

This paper investigates how the fluctuation-dissipation temperature in nonequilibrium systems depends on the observable chosen, linking this dependence to the entropy difference from equilibrium, with illustration on a mean-field model.

Contribution

It establishes a quantitative relation between observable dependence of temperature and entropy difference, highlighting a fundamental aspect of nonequilibrium thermodynamics.

Findings

Observable dependence occurs when phase-space distribution is non-uniform.

The dependence is quantitatively related to Shannon entropy difference.

Illustrated with a mean-field model with two heat baths.

Abstract

On general grounds, a nonequilibrium temperature can be consistently defined from generalized fluctuation-dissipation relations only if it is independent of the observable considered. We argue that the dependence on the choice of observable generically occurs when the phase-space probability distribution is non-uniform on constant energy shells. We relate quantitatively this observable dependence to a fundamental characteristics of nonequilibrium systems, namely the Shannon entropy difference with respect to the equilibrium state with the same energy. This relation is illustrated on a mean-field model in contact with two heat baths at different temperatures.