Spontaneous violation of symmetry of the classical Liouville equation

An exact solution to the classical Liouville equation is derived. It is found that it can have a partial solution with a broken symmetry with respect to time. Thus, in the general case, it does not follow from the invariance of the fundamental Liouville law concerning time reversal that the past and future play similar roles. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 85–89, August, 2007.