Tsallis thermostatics as a statistical physics of random chains

TL;DR

This paper demonstrates that Tsallis-Havrda-Charvát generalized statistics provides a useful framework for analyzing random chains, linking it to path integrals and physical models like polymers and relativistic particles.

Contribution

It introduces a novel application of Tsallis statistics to the statistical physics of random chains using path-integral methods and explores related transformation properties and ensembles.

Findings

Partition function corresponds to a fluctuating random loop in a potential.

Application to Schultz-Zimm polymer and relativistic particle models.

Discussion of transformation properties and grandcanonical ensembles.

Abstract

In this paper we point out that the generalized statistics of Tsallis-Havrda-Charv\'at 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-Charv\'at statistics are also briefly discussed.