Physical meaning of the parameters in the two-parameter (κ, ζ) generalized statistics

摘要

The physical meaning of the parameters (κ, ζ), emerging in the statistical theory [G. Kaniadakis, Eur. Phys. J. B 70 (2009) 3; D. P. Mittal, Metrika 22 (1975) 35; B. D. Sharma and I. J. Taneja, Metrika 22 (1975) 205] considered by Kaniadakis, is explained by considering the (κ, ζ)-kinetics of a particle system, in presence of an external force field F. By using the method [J. L. Du, Phys. Lett. A 329 (2004) 262] developed by Du, we show: First, the external force field necessarily induces in the system a temperature gradient ?T. Second, the parameters (κ, ζ) are univocally related to the magnitude and the angular separation of the vectors F and ?T. The achievements of the present paper have a general validity, holding independently on the particular approximation used to describe the collision term, in the equation governing the system evolution (i.e. Boltzmann or FokkerPlanck kinetics).