Dynamics of Energy Fluctuations in Equilibrating and Driven-Dissipative Systems

TL;DR

This paper derives universal expressions for energy fluctuations over time in systems that equilibrate or are driven to steady states, linking fluctuation size to energy flow properties.

Contribution

It provides new analytical formulas for energy fluctuation dynamics in both equilibrium and driven-dissipative systems, independent of microscopic details.

Findings

Energy fluctuation size depends only on average energy flows.

Derived expressions relate relaxation time, energy injection rate, and fluctuation magnitude.

Results apply to both equilibrium relaxation and non-equilibrium steady states.

Abstract

When two isolated system are brought in contact, they relax to equilibrium via energy exchange. In another setting, when one of the systems is driven and the other is large, the first system reaches a steady-state which is not described by the Gibbs distribution. Here, we derive expressions for the size of energy fluctuations as a function of time in both settings, assuming that the process is composed of many small steps of energy exchange. In both cases the results depend only on the average energy flows in the system, independent of any other microscopic detail. In the steady-state we also derive an expression relating three key properties: the relaxation time of the system, the energy injection rate, and the size of the fluctuations.