A complete derivation, from first principles, of the reaction-rate formula
for a generic process taking place in a heat bath of finite volume is given. It
is shown that the formula involves no finite-volume correction. Through
perturbative diagrammatic analysis of the resultant formula, the
detailed-balance formula is derived. The zero-temperature limit of the formula
is discussed. Thermal cutting rules, which are introduced in previous work, are
compared with those introduced by other authors.Comment: 35pages (text) plus 4pages (figures
