Conservative Force Fields in Non-Gaussian Statistics

Abstract

In this letter, we determine the -distribution function for a gas in the presence of an external field of force described by a potential U( r). In the case of a dilute gas, we show that the -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.