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

A simple model of particle creation and annihilation in an isolated assembly of particles with conserved energy and fixed volume, the Cell Model, is formulated. With increasing time, particle number distribution, obtained by averaging over many systems, approaches a time-independent, steady state distribution. Dependence of the steady state distribution on creation and annihilation conditional reaction probabilities is studied. The results obtained for the steady state are compared with predictions of statistical mechanics within the microcanonical ensemble. In general, the predictions of both models are different. They agree only if the creation and annihilation conditional probabilities are equal. This condition also results in the detailed balance in the steady state.