Conservative force fields in non-Gaussian statistics

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