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
S
N
= −k
B
∫
ρN
ln
(
h
ρN
N
)
dΓ
N
. 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.
