Tsallis uncertainty

TL;DR

This paper explores how systems described by Tsallis and other generalized entropies relate to modified uncertainty principles, revealing they may not obey the standard Heisenberg uncertainty principle and instead follow new forms.

Contribution

It introduces three new uncertainty principles linked to generalized entropies, including Tsallis entropy, and derives their associated energy-time relations and Unruh temperatures.

Findings

Generalized entropies can lead to modified uncertainty relations.

Systems with Tsallis entropy may violate the standard HUP.

New uncertainty principles are consistent with generalized entropy frameworks.

Abstract

It has been recently shown that the Bekenstein entropy bound is not respected by the systems satisfying modified forms of Heisenberg uncertainty principle (HUP) including the generalized and extended uncertainty principles, or even their combinations. On the other, the use of generalized entropies, which differ from Bekenstein entropy, in describing gravity and related topics signals us to different equipartition expressions compared to the usual one. In that way, The mathematical form of an equipartition theorem can be related to the algebraic expression of a particular entropy, different from the standard Bekenstein entropy, initially chosen to describe the black hole event horizon, see E. M. C. Abreu et al., MPLA 32, 2050266 (2020). Motivated by these works, we address three new uncertainty principles leading to recently introduced generalized entropies. In addition, the corresponding energy-time uncertainty relations and Unruh temperatures are also calculated. As a result, it seems that systems described by generalized entropies, such as those of Tsallis, do not necessarily meet HUP and may satisfy modified forms of HUP.