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Название: Entropy of irreversible cooling and the “discrimination” of model stochastic processes
Автор: Z. Alexandrowicz
Entropy changes are calculated for the irreversible cooling of a homogeneousN-particle system. The execution of an appropriate model stochastic process enables one to calculate the discriminationD (from the transition probabilities of the actual steps) and < –="" d=""> is shown to be equal to the external entropy change S ext. This is trivially true for the Metropolislike processes, where the individual particles maintain a direct heat exchange with a reservoir. Cooperative processes, which attribute the heat exchange to the mass ofN particlesin toto, are also considered; for these S ext is still equal to < –="" d="">. Hence, knowing and the entropy of the initial and final states of the system, one can calculate the net entropy production and study its minimization. Alternatively, a consistently probabilistic approach (independent of thermodynamic equivalents) postulates that statistical mechanical processes proceed with the least discrimination, Min, for given conditions. The postulate is supported by its conformance with the second law of thermodynamics. Min reduces to the Jaynes principle both at equilibrium and for isolated systems. Computer experiments illustrating the calculation ofD are presented. These describe the cooling of a square Ising lattice, with the help of the Metropolis and of the cooperative model processes; the latter, optimized for least entropy production, rapidly converge toward equilibrium.