Logical entropy and negative probabilities in quantum mechanics - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue 4open Année : 2022

Logical entropy and negative probabilities in quantum mechanics

Résumé

The concept of Logical Entropy, SL = 1-Σni=1 pi2, where the pi are normalized probabilities, was introduced by David Ellerman in a series of recent papers. Although the mathematical formula itself is not new, Ellerman provided a sound probabilistic interpretation of SL as a measure of the distinctions of a partition on a given set. The same formula comes across as a useful definition of entropy in quantum mechanics, where it is linked to the notion of purity of a quantum state. The quadratic form of the logical entropy lends itself to a generalization of the probabilities that include negative values, an idea that goes back to Feynman and Wigner. Here, we analyze and reinterpret negative probabilities in the light of the concept of logical entropy. Several intriguing quantum-like properties of the logical entropy are derived and discussed in finite dimensional spaces. For infinite-dimensional spaces (continuum), we show that, under the sole hypothesis that the logical entropy and the total probability are preserved in time, one obtains an evolution equation for the probability density that is basically identical to the quantum evolution of the Wigner function in phase space, at least when one considers only the momentum variable. This result suggest that the logical entropy plays a profound role in establishing the peculiar rules of quantum physics.Key words: Entropy / Negative Probabilities / Quantum Physics / Wigner Functions
Fichier principal
Vignette du fichier
fopen210012.pdf (519.02 Ko) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Licence : CC BY - Paternité

Dates et versions

hal-03545024 , version 1 (19-05-2023)

Identifiants

Citer

Giovanni Manfredi. Logical entropy and negative probabilities in quantum mechanics. 4open, 2022, 5, pp.8. ⟨10.1051/fopen/2022004⟩. ⟨hal-03545024⟩
46 Consultations
19 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More