... We have assumed that in statistical equilibrium, the probability distribution density depends only on the total energy. ... As it is shown in Refs. [1, 2], in a billiards, the probability distribution density as a function of time t (this function satisfies the classic Liouville equation) necessarily has the weak limit as t ±. ... The crucial idea of our approach is : transition to thermo dynamical (statistical) equilibrium is equal to replacement of the distribution (12) with its weak limit. ...
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