Quantum mechanical state preparation II-The statistical ensemble as a thermostat

In this sequel to an earlier paper on quantal state preparation (Park & Band, 1972), the simple model used before is adapted and somewhat generalised to enable an exact treatment of the causal evolution of a system immersed in a statistical ensemble constituted of replicas of the system itself. The ensemble is initially in a state of statistical equilibrium, but the initial state of the system is arbitrary. It is established as a purely dynamical theorem that the system is eventually coerced into the same equilibrium state as that of the replicas in the ensemble. From this general result we obtain as a special case mechanical justification for the common assumption in statistical thermodynamics that an ensemble can function as a thermostat.