Local fluctuation dissipation relation

TL;DR

This paper demonstrates that the local fluctuation dissipation relation can be derived from stochastic stability principles, showing that all sites in an aging system share the same effective temperature over time.

Contribution

It provides a theoretical derivation of the local fluctuation dissipation relation from stochastic stability, extending the understanding of effective temperatures in aging systems.

Findings

Local fluctuation dissipation relation follows from stochastic stability.

All sites in an aging system maintain the same effective temperature.

The derivation parallels the proof of the usual fluctuation dissipation theorem.

Abstract

In this letter I show that the recently proposed local version of the fluctuation dissipation relations follows from the general principle of stochastic stability in a way that is very similar to the usual proof of the fluctuation dissipation theorem for intensive quantities. Similar arguments can be used to prove that all sites in an aging experiment stay at the same effective temperature at the same time.