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

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Finite-temperature reaction-rate formula: Finite-volume system, detailed balance,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mn>0</mml:mn></mml:math>limit, and cutting rules

Finite-temperature reaction-rate formula: Finite-volume system, detailed balance,T→0limit, and cutting rules