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Physical meaning of the parameters in the two-parameter (\(\kappa\), \(\zeta\)) generalized statistics. (English) Zbl 1267.82074

Summary: The physical meaning of the parameters ({\(\kappa\)}, {\(\zeta\)}), emerging in the statistical theory considered, e.g., by G. Kaniadakis [Eur. Phys. J. B, Condens. Matter Complex Syst. 70, No. 1, 3–13 (2009; Zbl 1188.82034)], is explained by considering the ({\(\kappa\)}, {\(\zeta\)})-kinetics of a particle system, in the presence of an external force field \(\mathbf{F}\). By using a method developed by J. Du [Phys. Lett., A 329, No. 4–5, 262–267 (2004; Zbl 1209.82039)], we show first that the external force field necessarily induces in the system a temperature gradient \(\nabla T\) and that, secondly, the parameters ({\(\kappa\)}, {\(\zeta\)}) are univocally related to the magnitude and the angular separation of the vectors \(\mathbf{F}\) and \(\nabla T\). 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 Fokker-Planck kinetics).

MSC:

82C03 Foundations of time-dependent statistical mechanics
82C22 Interacting particle systems in time-dependent statistical mechanics
35Q20 Boltzmann equations
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