Method of Transition Probabilities in Quantum Mechanics and Quantum Statistics

The concepts microscopic reversibility, detailed balancing, equal probabilities, equilibrium, $H$ theorem are often used in (coarse grained) quantum statistics. It is pointed out that each has a (fine grained) quantum-mechanical counterpart. These concepts are formulated, and their interrelations discussed, at an abstract mathematical level. The results are then interpreted by taking first the fine grained and then the coarse grained point of view. A type of transition matrix arises which does not seem to have been investigated so far, and some of its properties are discussed.