Bekenstein bound and uncertainty relations

Physics Letters B, vol. 824, pp. 136818

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.

Authors 4

1. Luca Buoninfante

   Tokyo Institute of Technology

   Affiliation as printed

   Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan

   Tokyo Institute of Technology;

2. Giuseppe Gaetano Luciano

   University of Salerno · Istituto Nazionale di Fisica Nucleare · Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Salerno

   Affiliation as printed

   Dipartimento di Fisica, Università di Salerno, Via Giovanni Paolo II, 132, I-84084 Fisciano (SA), Italy

   INFN, Sezione di Napoli, Gruppo collegato di Salerno, Italy

   Istituto Nazionale di Fisica Nucleare

3. Luciano Petruzziello

   University of Salerno · Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Salerno

   Affiliation as printed

   Dipartimento di Ingegneria, Università di Salerno, Via Giovanni Paolo II, 132, I-84084 Fisciano (SA), Italy

   INFN, Sezione di Napoli, Gruppo collegato di Salerno, Italy

   University of Salerno

4. Fabio Scardigli corresponding Aachen Institute-Lorentz for Theoretical Physics

   Leiden University · National Taiwan University · Politecnico di Milano

   Affiliation as printed

   Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy

   Institute-Lorentz for Theoretical Physics, Leiden University, P.O. Box 9506, Leiden, The Netherlands

   National Taiwan University