Hierarchy of Times for the Establishment of the Gibbs Distribution

Abstract

It is shown that there are three characteristic time scales for the establishment of thermodynamic equilibrium: the time for the thermalization of the system; the time for establishing a uniform temperature in the system after contact with the thermostat; and, finally, the time for establishing full ergodicity in the system. The first time is determined by particle collisions (in fluids) or multiphonon processes (in condensed media) and lies in the range from tens of picoseconds (in dense fluids) to microseconds (in pure crystals at low temperatures). The second time is determined by the thermal diffusivity and the size of the system and, for millimeter-sized samples, lasts for seconds. The third time is determined by the particle diffusion rates and can vary from hundreds of picoseconds (in gases and liquids) to astronomical times (in solids at low temperatures). The concept of ergodicity as applied to crystals and glasses is discussed.