Effective temperature in nonequilibrium steady states of Langevin systems with a tilted periodic potential

TL;DR

This paper investigates the effective temperature in nonequilibrium Langevin systems with tilted periodic potentials, revealing that a parameter called  plays the role of temperature in large-scale descriptions, distinct from the environment temperature.

Contribution

The study derives a large-scale description of the probability density in modulated Langevin systems, showing  as an effective temperature measurable without direct diffusion or mobility measurements.

Findings

 acts as an effective temperature in large-scale descriptions.

 can be experimentally determined directly.

The ratio of diffusion to mobility deviates from the environmental temperature far from equilibrium.

Abstract

We theoretically study Langevin systems with a tilted periodic potential. It has been known that the ratio $\Theta$ of the diffusion constant to the differential mobility is not equal to the temperature of the environment (multiplied by the Boltzmann constant), except in the linear response regime, where the fluctuation dissipation theorem holds. In order to elucidate the physical meaning of $\Theta$ far from equilibrium, we analyze a modulated system with a slowly varying potential. We derive a large scale description of the probability density for the modulated system by use of a perturbation method. The expressions we obtain show that $\Theta$ plays the role of the temperature in the large scale description of the system and that $\Theta$ can be determined directly in experiments, without measurements of the diffusion constant and the differential mobility.