Non-extensive entropy from incomplete knowledge of Shannon entropy?

TL;DR

This paper interprets Tsallis' nonextensive entropy as a consequence of incomplete knowledge about a system, proposing it is derived rather than fundamental, which may resolve some issues in its original interpretation.

Contribution

It offers an information-theoretic interpretation of Tsallis' entropy, framing it as arising from incomplete system knowledge rather than as a fundamental concept.

Findings

Tsallis' entropy can be viewed as derived from incomplete information.

This interpretation addresses some problems in the original Tsallis framework.

Provides a new perspective on nonextensive statistical mechanics.

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.