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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Tsallis thermostatics as a statistical physics of random chains
Petr Jizba1,2, Jan Korbel1,3, Václav Zatloukal1,4
1Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1, Czech Republic.
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 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.
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