The kappa parameter and kappa-distribution in kappa-deformed statistics for the systems in an external field

TL;DR

This paper derives a physical interpretation of the kappa parameter in kappa-deformed statistics, linking it to temperature gradients and external forces, and discusses its applicability to nonequilibrium stationary states in external fields.

Contribution

It provides a formula for the kappa parameter based on the kappa-H theorem and generalized Boltzmann equation, offering a new physical understanding of kappa-deformed statistics.

Findings

Kappa parameter relates to temperature gradient and external force.

Kappa-distribution describes nonequilibrium stationary states.

Suitable for systems in external fields with specific force-temperature configurations.

Abstract

The kappa-deformed statistics has been studied in many papers. It is naturally important question for us to ask what should the kappa parameter stand for and under what physical situation should the kappa-deformed statistics be suitable for the statistical description of a system. In this paper, we have derived a formula expression of kappa parameter based on the kappa-H theorem, the kappa-velocity distribution and the generalized Boltzmann equation in the framework of kappa-deformed statistics. We thus obtain a physical interpretation for the kappa parameter different from zero with regard to the temperature gradient and the external force field. We show that, as the q-statistics based on Tsallis entropy, the kappa-deformed statistics may also be the candidate one suitable for the statistical description of the systems in external fields when being in the nonequilibrium stationary state, but has different physical characteristics. Namely, the kappa-distribution is found to describe the nonequilibrium stationary state of the system where the external force should be vertical to the temperature gradient.