Nonextensive kinetic theory and H-theorem in general relativity

Abstract

The nonextensive kinetic theory for degenerate quantum gases is discussed in the general relativistic framework. By incorporating nonadditive modifications in the collisional term of the relativistic Boltzmann equation and entropy current, it is shown that Tsallis entropic framework satisfies a H-theorem in the presence of gravitational fields. Consistency with the 2nd law of thermodynamics is obtained only whether the entropic q-parameter lies in the interval q ∈ [0, 2]. As occurs in the absence of gravitational fields, it is also proved that the local collisional equilibrium is described by the extended Bose-Einstein (Fermi-Dirac) q-distributions.

Analytic approaches of the anomalous diffusion: A review

“…We show that these equations gain a foundation when they are involved with the proposal of non-extensive statistical mechanics [31]. Nowadays, the Tsallis statistic [31] and nonlinear diffusion have assumed important roles in the application of more subtle problems in thermodynamics, such as black holes [21,143], generalised forms of H-theorem [19,20,144], financial market [145,146], and many other systems [94,147,148]. Here, it is worth mentioning to the reader that from the point of view of the H theorem [11] the porous media equations may imply the Tsallis entropy.…”