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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

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Abstract

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 \(q\rightarrow 1/3\), 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 \(q\rightarrow 1/3\), 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.

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Acknowledgements

F. E. M. Silveira is partially supported by São Paulo Research Foundation (FAPESP) under Grant Number 17/20192-2. M. H. Benetti is supported by Federal University of ABC (UFABC) under a PhD scholarship.

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  1. Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Rua Santa Adélia, 166, Bairro Bangu, CEP 09210-170, Santo André, SP, Brazil

    F. E. M. Silveira & M. H. Benetti

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Silveira, F.E.M., Benetti, M.H. Towards a physical interpretation of the deformation parametrization in nonextensive statistics. Eur. Phys. J. Plus 136, 1212 (2021). https://doi.org/10.1140/epjp/s13360-021-02233-x

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