Tsallis thermostatics as a statistical physics of random chains

Abstract

In this paper we point out that the generalized statistics of Tsallis-Havrda-Charvát can be conveniently used as a conceptual framework for statistical treatment of random chains. In particular, we use the path-integral approach to show that the ensuing partition function can be identified with the partition function of a fluctuating oriented random loop of arbitrary length and shape in a background scalar potential. To put some meat on the bare bones, we illustrate this with two statistical systems; Schultz-Zimm polymer and relativistic particle. Further salient issues such as the $PSL(2;R)$ transformation properties of Tsallis' inverse-temperature parameter and a grandcanonical ensemble of fluctuating random loops related to the Tsallis-Havrda-Charvát statistics are also briefly discussed.

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• q-generalized Tsallis thermostatistics in Unruh effect for mixed fields
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• Inflation Based on the Tsallis Entropy
• Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: new route to non-extensive thermostatistics
• On Statistical Properties of Jizba-Arimitsu Hybrid Entropy
• Rescaling the nonadditivity parameter in Tsallis thermostatistics
• Role of chemical potential at kinetic freeze-out using Tsallis non-extensive statistics in proton-proton collisions at the Large Hadron Collider
• Analysis of Tsallis' classical partition function's poles
• Rescuing the MaxEnt treatment for $q$-generalized entropies
• Verlinde's emergent gravity in an $\mathbf{n}-$dimensional, non-additive Tsallis' scenario
• q-Path entropy phenomenology for phase-space curves
• Decoherence limit of quantum systems obeying generalized uncertainty principle: new paradigm for Tsallis thermostatistics