A heuristic generalization of the Boltzmann-Gibbs microcanonical entropy isproposed, able to describe meta-equilibrium features and evolution ofmacroscopic systems. Despite its simple-minded derivation, such a function of"collective parameters" characterizing the microscopic state of N-body systems,yields, at one time, a statistical interpretation of dynamic evolution, anddynamic insights on the basic assumption of statistical mechanics. Its natural(implicit) time dependence entails} a "Second Law-like" behaviour and allowsmoreover, to perform an elementary test of the Loschmidt reversibilityobjection, pointing out the crucial relevance of Chaos in setting up effective(statistico-mechanical and dynamical) "arrows of time". Several concrete(analytical and numerical) applications illustrate its properties.
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