Why does statistical mechanics ‘work’ in condensed matter?

Abstract

Abstract The reasons behind the possibility of using the Gibbs distribution in condensed matter are considered. While the basics of statistical mechanics in gases are covered in great detail in many textbooks and reviews, the reasons for using the Gibbs distribution in crystals, glasses, and liquids are rarely considered. Most textbooks still only speak of a qualitative replacement of the mechanical description with a statistical one when considering a very large number of particles. At the same time, it turns out that the Gibbs distribution is not formally applicable to a harmonic crystal of a large number of particles. However, a system of even a small number of coupled anharmonic oscillators can demonstrate all the basic features of thermodynamically equilibrium crystals and liquids. It is the nonlinearity (anharmonism) of vibrations that leads to the mixing of phase trajectories and ergodicity of condensed matter. When the system goes into a state of thermodynamic equilibrium, there are 3 characteristic time scales: the time of thermalization of the system (in fact, the time of establishment of the local Gibbs distribution in momentum space and establishment of the local temperature); the time of establishment of a uniform temperature in the system after contact with the thermostat; and, finally, the time of establishment of ergodicity in the system (in fact, the time of ‘sweeping’ the entire phase space, including its coordinate part). The genesis of defect formation and diffusion in crystals and glasses, as well as their ergodicity, is discussed.