Non-extensive entropy from incomplete knowledge of Shannon entropy?

Abstract

In this paper we give an interpretation of Tsallis' nonextensive statistical mechanics based upon the information-theoretic point of view of Luzzi et al. [cond-mat/0306217; cond-mat/0306247; cond-mat/0307325], suggesting Tsallis' entropy to be not a fundamental concept but rather a derived one, stemming from an incomplete knowledge of the system, not taking properly into account its interaction with the environment. This interpretation seems to avoid some problems occurring with the original interpretation of Tsallis statistics.

v.4. 11 pages. Title changed. Content substantially changed: added discussion of several points raised by various referees and readers; Also reference made to work by Luzzi, Vasconcellos, Galvao Ramos. Physica Scripta, to appear