Conservative Force Fields in Non-Gaussian Statistics

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($\mathbf{r}$). 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.

10 pages, 1 figure

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