The two parameters (k, r) in the generalized statistics

TL;DR

This paper explores a two-parameter generalized statistical framework derived from the Boltzmann equation, linking parameters to system characteristics and extending previous models like Tsallis statistics for complex systems.

Contribution

It introduces a new two-parameter generalized statistics connecting parameters to physical quantities, broadening the applicability of statistical models for complex systems.

Findings

Parameters (k, r) relate to system characteristics.

The model recovers Tsallis statistics as a special case.

Potential to describe complex systems more effectively.

Abstract

Based on the generalized Boltzmann equation and the reverse function of the distribution function, we investigate the two-parameter generalized statistics and get an expression between the two parameters (k,r) and the physical quantities about the system considered. We find that the two parameters can define some characteristics of the system. As examples, this result can just return to the previous one obtained for Tsallis and statistics. For some complex systems, we may need the two-parameter statistics to describe.