Markov Processes and the H-Theorem

The H -theorem is investigated in view of Markov processes. The proof is valid even in the fields other than physics, since none of physical relations, such as the principle of microscopic reversibility, the unitarity of S -matrix and so on, is utilized. The well-known ` Wiederkehreinwand ' is also re-examined from this standpoint of view and a reconciliation is regained between the H -theorem and the recurrence in the sense of probability theory.