Concerning the Entropy Expression of the Uncertainty Principle

Rupert L. Frank, Élliott H. Lieb

Roy B. Leipnik

Roy B. Leipnik

Julius Sumner Miller

Imen Ali Kallel, A. Saoudi

In this paper, we present the localization of the ν-entropy for the Weinstein Gabor transform. Through the utilization of the ν-entropy, we establish an alternative expression for the Heisenberg uncertainty principle for the Weinstein Gabor transform. In addition, we further extend our study by elaborating on an Lp version of the Heisenberg uncertainty principle for the Weinstein Gabor transform.

Vladimír Majerník, Eva Majerníková, Serge Shpyrko

Abstract Besides the well-known Shannon entropy, there is a set of Shannon-like entropies which have applications in statistical and quantum physics. These entropies are functions of certain parameters and converge toward Shannon entropy when these parameters approach the value 1. We describe briefly the most important Shannon-like entropies and present their graphical representations. Their graphs look almost identical, though by superimposing them it appears that they are distinct and characteristic of each Shannon-like entropy. We try to formulate the alternative entropic uncertainty relations by means of the Shannon-like entropies and show that all of them equally well express the uncertainty principle of quantum physics.