Tsallis thermostatics as a statistical physics of random chains

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...

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Bibliographic Details
Published in:Physical review. E 2017-02, Vol.95 (2-1), p.022103-022103, Article 022103
Main Authors: Jizba, Petr, Korbel, Jan, Zatloukal, Václav
Format: Article
Language:English
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Summary: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 projective special linear group PSL(2,R) transformation properties of Tsallis' inverse-temperature parameter and a grand-canonical ensemble of fluctuating random loops related to the Tsallis-Havrda-Charvát statistics are also briefly discussed.
ISSN:2470-0045
2470-0053
DOI:10.1103/PhysRevE.95.022103