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). 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.

It is shown that the comment by Costa and Meneses [1] did not point any technical or conceptual flaw in our paper titled "Conservative Force Fields in Nonextensive Kinetic Theory" (Physica A 316, 289 (2002)). In particular, the application of the nonextensive distribution to the historical problem of the unbounded isothermal atmosphere under constant gravity is theoretically correct. It should be stressed that our solution is somewhat connected with a similar solution to a problem appearing in the astrophysical domain, namely, the so-called singular isothermal sphere. Actually, both problems are solved * limajas@dfte.ufrn.br † zero@dfte.ufrn.br ‡ rsilva@uern.br by a stationary Tsallis q-distribution with a "thermal cut-off" in the allowed values of the energy.