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A simple model of particle creation and annihilation in an isolated assemblyof particles with conserved energy and fixed volume, the Cell Model, isformulated. With increasing time, particle number distribution, obtained byaveraging over many systems, approaches a time-independent, steady statedistribution. Dependence of the steady state distribution on creation andannihilation conditional reaction probabilities is studied. The resultsobtained for the steady state are compared with predictions of statisticalmechanics within the microcanonical ensemble. In general, the predictions ofboth models are different. They agree only if the creation and annihilationconditional probabilities are equal. This condition also results in thedetailed balance in the steady state.

Steady state of isolated systems versus microcanonical ensemble in cell model of particle creation and annihilation