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.
KeywordsPhase Trajectory Liouville Equation Spontaneous Violation Probabilistic Determinism Lagrangian Factor
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