Information Theory and the Approach to Equilibrium

Abstract

After a general discussion of thermodynamic equilibrium and the information-theoretic formulation of equilibrium statistical mechanics, illustrative calculations are presented of the evolution to equilibrium of a finite segment (the system) of an infinite coupled harmonic-oscillator chain, most of which is regarded as the heat bath. The reduced Liouville function ρN is used to define the information-theoretic version of the Gibbs entropy as SN = −kB ∫ ρN ln(hρNN)dΓN. This entropy evolves to a proper equilibrium value as |t| → ∞ from time-reversible dynamics, because ρN spreads from an initially sharp distribution to a diffuse one characteristic of the heat bath in equilibrium. The approach is regarded as generally valid, in principle, although the procedure is most easily carried out in the treatment of coupled harmonic-oscillator systems.