Bekenstein bound and uncertainty relations

TL;DR

This paper investigates how the Bekenstein bound, which limits entropy in quantum systems, is modified when the Heisenberg Uncertainty Principle is deformed to include gravitational effects near the Planck scale, leading to a generalized bound.

Contribution

It introduces a generalized Bekenstein bound derived from a deformed uncertainty relation that accounts for gravitational effects at the Planck scale.

Findings

Generalized Bekenstein bound derived for deformed uncertainty relations.

Implications discussed for positive and negative deformation parameters.

Results connect quantum gravity effects with entropy bounds.

Abstract

The non zero value of Planck constant $h$ underlies the emergence of several inequalities that must be satisfied in the quantum realm, the most prominent one being Heisenberg Uncertainty Principle. Among these inequalities, Bekenstein bound provides a universal limit on the entropy that can be contained in a localized quantum system of given size and total energy. In this Letter, we explore how Bekenstein bound is affected when Heisenberg uncertainty relation is deformed so as to accommodate gravitational effects close to Planck scale (Generalized Uncertainty Principle). By resorting to general thermodynamic arguments, and in regimes where the equipartition theorem still holds, we derive in this way a "generalized Bekenstein bound". Physical implications of this result are discussed for both cases of positive and negative values of the deformation parameter.