Thermodynamic Framework for Compact q-Gaussian Distributions

Abstract

Recent works have associated systems of particles, characterized by short-range repulsive interactions and evolving under overdamped motion, to a nonlinear Fokker-Planck equation within the class of nonextensive statistical mechanics, with a nonlinear diffusion contribution whose exponent is given by $\nu =2-q$. The particular case $\nu =2$ applies to interacting vortices in type-II superconductors, whereas $\nu >2$ covers systems of particles characterized by short-range power-law interactions, where correlations among particles are taken into account. In the former case, several studies presented a consistent thermodynamic framework based on the definition of an effective temperature $\theta$ (presenting experimental values much higher than typical room temperatures $T$, so that thermal noise could be neglected), conjugated to a generalized entropy $s_{\nu }$ (with $\nu =2$). Herein, the whole thermodynamic scheme is revisited and extended to systems of particles interacting repulsively, through short-ranged potentials, described by an entropy $s_{\nu }$, with $\nu >1$, covering the $\nu =2$ (vortices in type-II superconductors) and $\nu >2$ (short-range power-law interactions) physical examples. The main results achieved are: (a) The definition of an effective temperature $\theta$ conjugated to the entropy $s_{\nu }$; (b) The construction of a Carnot cycle, whose efficiency is shown to be $\eta =1-({\theta }_2/{\theta }_1)$, where ${\theta }_1$ and ${\theta }_2$ are the effective temperatures associated with two isothermal transformations, with ${\theta }_1>{\theta }_2$; (c) Thermodynamic potentials, Maxwell relations, and response functions. The present thermodynamic framework, for a system of interacting particles under the above-mentioned conditions, and associated to an entropy $s_{\nu }$, with $\nu >1$, certainly enlarges the possibility of experimental verifications.

18 pages, 1 figure

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Cited by in corpus (7)

• Analytic approaches of the anomalous diffusion: a review
• Unidirectional Random Growth with Resetting
• Fractional Fokker-Planck equation from non-singular kernel operators
• Overdamped dynamics of particles with repulsive power-law interactions
• Phase space volume scaling of generalized entropies and anomalous diffusion scaling governed by corresponding non-linear Fokker-Planck equations
• Features of constrained entropic functional variational problems
• Non-linear Fokker-Planck equations from conformal metrics and scalar curvature