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 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.