The Statistical Mechanical Aspect of the H-Theorem, II

This paper is devoted to the discussion of the properties of the H-function, especially concerning its irreversible character somewhat quantitatively, usin.g the sarne model as that used in the previous paper. As the result, it is concluded that the more roughly the macroscopic obsen·ation is done, the more rapidly the H-function decreases to an equilibrium value as shown 111 Fig. 2. Thus it is clarified that H-function of a given system which is in a non-equilibrium situation should be defined in connec-tion with the accuracy of macroscopic observations. In our calculations, we have not used any assump-tions such as "Stosszahlansatz " or the ccarse-graming in every rr.oment of the process, except only once in setting. up the ensemble which represents a given non-equilibrium.initial state. Our res:ult gives a justification of statistical aspect of the H-theorem suggested by Ehrenfest without proof