The approach to equilibrium for systems interacting with their environment by being regularly exposed to low energy, low intensity pulses of some type of quanta is studied. Assuming a randomness condition on the interaction of these quanta with the system, but making no assumptions about the accessible states of the system, we show that microcanonical equilibrium is reached. Although the intensity of the pulses is assumed to be weak the interactions are treated exactly, with no recourse to perturbation theory. The origin of time asymmetry and the absence of recurrence is discussed
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