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In this paper we point out that the generalized statistics ofTsallis-Havrda-Charv\'at can be conveniently used as a conceptual framework forstatistical treatment of random chains. In particular, we use the path-integralapproach to show that the ensuing partition function can be identified with thepartition function of a fluctuating oriented random loop of arbitrary lengthand shape in a background scalar potential. To put some meat on the bare bones,we illustrate this with two statistical systems; Schultz-Zimm polymer andrelativistic particle. Further salient issues such as the $PSL(2;R)$transformation properties of Tsallis' inverse-temperature parameter and agrandcanonical ensemble of fluctuating random loops related to theTsallis-Havrda-Charv\'at statistics are also briefly discussed.

Tsallis thermostatics as a statistical physics of random chains