Towards a physical interpretation of the deformation parametrization in nonextensive statistics Evidence for a generalization of the number of degrees of freedom in a nonextensive gas of charged particles

Autor(es)

Silveira, F. E. M. ^[1] ; Benetti, M. H. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Fed ABC, Ctr Ciencias Nat & Humanas, Rua Santa Adelia 106, BR-09210170 Santo Andre, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: EUROPEAN PHYSICAL JOURNAL PLUS; v. 136, n. 12 DEC 6 2021.
• Citações Web of Science: 0

Resumo

We explore new ways to interpret the role played by the deformation q-parameter in nonextensive statistics. A generalized polytropic gamma-index is deduced with basis on the Tsallis distribution. In the limit q -> 1/3, it is shown that the gamma-index decreases hyperbolically with the increase of the concentration n of charged particles in a nonextensive gas. An equation of state of a nonextensive system is derived following the generalized polytropic index. In the limit q -> 1/3, it is found that a constant and uniform isotropic pressure develops throughout a nonextensive gas of charged particles in the absence of electric and magnetic fields, and in a stationary state of equilibrium of the system. The usual reduction of the Tsallis to Kappa distributions is examined with basis on their corresponding equations of state. It is shown that such a procedure leads to a general proof of the relationship between the q-parameter and spectral kappa-index, and between the T-Maxwellian and Theta-Kappa temperatures. A generalization of the number of degrees of freedom in a nonextensive gas is provided. It is suggested that a nonextensive polytropic process might characterize a system that shall be something between a monoatomic gas with more than three translational degrees of freedom, and a diatomic gas with less than three translational plus two rotational degrees of freedom. Moreover, it is proved that the restriction of the Tsallis to Kappa distributions requires that the bulk concentration n in a nonextensive gas does not exceed 50% of the concentration n(0) on its boundary, thereby characterizing a low-density system. Possible applications of our theory to anisotropic structures are briefly addressed. (AU)

• Processo FAPESP: 17/20192-2 - Análise de Estabilidade em Tokamaks de Grande Razão de Aspecto: Relaxamento Finito da Corrente devido à Inércia dos Elétrons
• Beneficiário: Francisco Eugenio Mendonça da Silveira
• Modalidade de apoio: Auxílio à Pesquisa - Regular