A REMARK ON H THEOREM

It is pointed out that the quantum-mechanical Boltzmann H theoremin the restricted sense(i.e.with explicit consideration of the statistics of theparticles constituting the assembly and their interactions)does not leaddirectly to the distribution laws for the particles among their various statesas is commonly believed,but to the equality of the probability for all statesbelonging to the assembly as a whole if the assembly is isolated(or to theBoltzmann factor for the probabilities of states belonging to an assemblykept at constant temperature),in agreement with the result of the generaliz-ed quantum-mechanical H theorem as given by Pauli.The distributionlaws for the particles among their various states may,of course,be deducedfrom the latter.In the course of proof,we have also introduced the following minorimprovements:(1)To avoid the restriction due to the conservation of energy inmicroscopic processes which lead to changes in the states of the particlesand thus to equilibrium,we let our assembly be in interaction with a heatreservoir,so that energies may be supplied by or given to it.This istautomount to changing the study of the entropy for an isolated assembly tothat of the free energy for an assembly kept at constant temperature.(2)Interaction energies between the particles which affect the totalenergy of the system and also the distribution laws for the particles areincluded.