ENERGY-FLOW, PARTIAL EQUILIBRATION, AND EFFECTIVE TEMPERATURES IN SYSTEMS WITH SLOW DYNAMICS

We show that, in nonequilibrium systems with small heal flows, there i s a time-scale-dependent effective temperature that plays the same rol e as the thermodynamical temperature in that it controls the direction of heat flows and acts as a criterion for thermalization. We simultan eously 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 ex amples taken from solvable models with nontrivial low-temperature dyna mics, but argue that they have a much wider range of validity. We sugg est experimental checks of these ideas.