Fluctuation-dissipation relations in driven dissipative systems

TL;DR

This paper provides exact theoretical results on how fluctuation-dissipation relations are violated in driven dissipative systems, showing the dependence of fluctuation temperature on measurement time and its distinction from environmental and granular temperatures.

Contribution

It offers a precise theoretical analysis of fluctuation-dissipation violations and introduces a fluctuation temperature that varies with measurement time in driven dissipative systems.

Findings

Fluctuation temperature depends on measurement time.

Fluctuation temperature differs from environmental and granular temperatures.

Time independence of fluctuation temperature explained for simple measurements.

Abstract

Exact theoretical results for the violation of time dependent fluctuation-dissipation relations in driven dissipative systems are presented. The ratio of correlation to delayed response in the stochastic model introduced in [Phys. Rev. Lett. 93, 240601 (2004)] is shown to depend on measurement time. The fluctuation temperature defined by this ratio differs both from the temperature of the environment performing the driving, and from other effective temperatures of the system, such as the average energy (or "granular temperature"). General explanations are given for the time independence of fluctuation temperature for simple measurements or long measurement times.