In order to study analytically the nature of the size separation in granular mixture, we present the maximum entropy production principle based on kinetic temperature of granular mixture. For simplicity we apply this principle to size separation of a sphere binary mixture in vibrated bed, and we find a new thermodynamic mechanism of size separation phenomenon. With the irreversible processes such as elastic collisions and frictions, the kinetic energy is dissipated rapidly in system, which induces the entropy production. By the fact that the entropy production rate always has the absolute maximum at the stable state of granular mixture, we find the crossover from "Brazil Nut Effect" to its reverse by changing particles size and density, and our result is about satisfied with Schnautz's experiment.
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