Energy flow, partial equilibration and effective temperatures in systems with slow dynamics

TL;DR

This paper demonstrates that in nonequilibrium systems with slow dynamics, an effective temperature dependent on time scale governs heat flow and thermalization, unifying stationary and aging behaviors.

Contribution

It introduces a unified framework for effective temperatures in slow, nonequilibrium systems, applicable to both stationary and aging regimes, supported by solvable model examples.

Findings

Effective temperature controls heat flow direction.

Similar behavior in stationary and aging systems when expressed via correlations.

Proposes experimental tests for the theoretical predictions.

Abstract

We show that, in nonequilibrium systems with small heat flows, there is a time-scale dependent effective temperature which plays the same role as the thermodynamical temperature, in that it controls the direction of heat flows and acts as a criterion for thermalization. We simultaneously treat the case of stationary systems with weak stirring and of glassy systems that age after cooling and show that they exhibit very similar behavior provided that time dependences are expressed in terms of the correlations of the system. We substantiate our claims with examples taken from solvable models with non-trivial low-temperature dynamics, but argue that they have a much wider range of validity. We suggest experimental checks of these ideas.