Abstract

The statistical theory based on the parametric family of Rényi entropy functionals is a generalization of Gibbs statistics. Depending on the value of the involved parameter, the corresponding Rényi distribution can take both an exponential form and a power-law form, which is typical for a wide range of statistical models. In this paper, we prove the energy equipartition theorem in the case of Rényi 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 Rényi distribution, which represents a generalization of a power-low distribution and thus allows us to approximate some empirical data more precisely, has been studied.

中文翻译：

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基于Rényi熵的统计物理中的某些关系

摘要

基于Rényi熵泛函的参数族的统计理论是Gibbs统计的概括。取决于所涉及参数的值，相应的Rényi分布既可以采用指数形式，也可以采用幂律形式，这是广泛的统计模型所特有的。在本文中，我们证明了在Rényi统计情况下的能量均分定理，这使得解决大量经典统计模型获得平均能量的问题成为可能。将计算出的平均能量的建议方法与直接计算最简单的低功耗哈密顿量系统的该量的过程进行了比较。提出了新的关系，可以简化所考虑理论中的计算。Rényi发行的一个特例，