Calculational Rules for Evaluating Transition Rates of Reactions Taking Place in a Closed System

Abstract Systematic calculational rules for evaluating the reaction rate of a generic dynamical process taking place in a closed system are presented. As applications, various reactions in the early universe and in the quark-gluon plasma are kept in mind. In the systems of practical interest, VE 3 ⪢ 1 holds, with E the energy and V the volume of the system. In such cases, the reaction rate is found to be expanded in powers of l/( VE 3 ) 1/4 , and each term of the series is written in terms of the corresponding finite-temperature reaction rate and the Helmholtz free energy at the temperature T , both of which have been extensively studied so far. The temperature T is related to E through the generalized Stefan-Boltzmann law. The rules are applied to the toy example, calculation of the production rate of a heavy scalar from a closed system of light scalars.