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 $\mathrm{PSL}(2,\mathbb{R})$ 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.

• Received 28 October 2016

DOI:https://doi.org/10.1103/PhysRevE.95.022103