Certain Relations in Statistical Physics Based on Renyi Entropyстатья
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Дата последнего поиска статьи во внешних источниках: 29 апреля 2021 г.
Аннотация:The statistical theory based on the parametric family of Re´nyi entropy functionals is a generalization of Gibbs statistics. Depending on the value of the involved parameter, the corresponding Re´nyi distribution can take both an exponential form and a power-law form, which is typical for a widerange of statistical models. In this paper, we prove the energy equipartition theorem in the case of Re´nyi statistics, which makes it possible to solve the problem of obtaining the average energy for a large number of classical statistical models. The proposed approach for calculating the average energy is compared with the procedure for directly calculating this quantity for a system described by the simplest power-low Hamiltonian. New relations are presented that simplify the calculations in the considered theory. A special case of the Re´nyi distribution, which represents a generalization of a power-low distribution and thus allows us to approximate some empirical data more precisely, has been studied.