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

Abstract

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