Conservative Force Fields in Non-Gaussian Statistics

TL;DR

This paper derives a $$-distribution function for gases under external force fields using kinetic theory, highlighting the role of long-range interactions in Kaniadakis thermostatistics.

Contribution

It provides a rigorous derivation of the $$-power law distribution with potential energy factors within the kinetic theory framework.

Findings

Derivation of the $$-distribution function in external fields

Inclusion of potential energy factors in the distribution

Implications for long-range interactions in thermostatistics

Abstract

In this letter, we determine the $\kappa$-distribution function for a gas in the presence of an external field of force described by a potential U(${\bf r}$). In the case of a dilute gas, we show that the $\kappa$-power law distribution including the potential energy factor term can rigorously be deduced in the framework of kinetic theory with basis on the Vlasov equation. Such a result is significant as a preliminary to the discussion on the role of long range interactions in the Kaniadakis thermostatistics and the underlying kinetic theory.