Entropy evolution as a guide for replacing the Liouville equation

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Abstract
A replacement is proposed for the usual Liouville equation for the evolution of the distribution function of a statistical ensemble of classical, homogeneously thermostatted systems. The correct description of the entropy evolution is an essential criterian for such a replacement to satisfy, since we show from numerical realizations of a physically realistic model system that the Liouville equation is not satisfactory in general. On the other hand, both the Liouville equation and the proposed replacement correctly describe the evolution of ordinary mechanical observables, such as the energy. The particular form of the proposed replacement is shown to describe correctly a variety of experimental conditions.

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