Role of Quantum Entropy and Establishment of H-Theorems in the Presence of Graviton Sinks for Manifestly-Covariant Quantum Gravity

Based on the introduction of a suitable quantum functional, identified here with the Boltzmann–Shannon entropy, entropic properties of the quantum gravitational field are investigated in the framework of manifestly-covariant quantum gravity theory. In particular, focus is given to gravitat...

Full description

Bibliographic Details
Main Authors: Massimo Tessarotto, Claudio Cremaschini
Format: Article
Language:English
Published: MDPI AG 2019-04-01
Series:Entropy
Subjects:
Online Access:https://www.mdpi.com/1099-4300/21/4/418
id doaj-311a1b1831684109975265a873fbfe04
record_format Article
spelling doaj-311a1b1831684109975265a873fbfe042020-11-24T21:46:51ZengMDPI AGEntropy1099-43002019-04-0121441810.3390/e21040418e21040418Role of Quantum Entropy and Establishment of H-Theorems in the Presence of Graviton Sinks for Manifestly-Covariant Quantum GravityMassimo Tessarotto0Claudio Cremaschini1Department of Mathematics and Geosciences, University of Trieste, Via Valerio 12, 34127 Trieste, ItalyInstitute of Physics and Research Center for Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám.13, CZ-74601 Opava, Czech RepublicBased on the introduction of a suitable quantum functional, identified here with the Boltzmann–Shannon entropy, entropic properties of the quantum gravitational field are investigated in the framework of manifestly-covariant quantum gravity theory. In particular, focus is given to gravitational quantum states in a background de Sitter space-time, with the addition of possible quantum non-unitarity effects modeled in terms of an effective quantum graviton sink localized near the de Sitter event horizon. The theory of manifestly-covariant quantum gravity developed accordingly is shown to retain its emergent-gravity features, which are recovered when the generalized-Lagrangian-path formalism is adopted, yielding a stochastic trajectory-based representation of the quantum wave equation. This permits the analytic determination of the quantum probability density function associated with the quantum gravity state, represented in terms of a generally dynamically-evolving shifted Gaussian function. As an application, the study of the entropic properties of quantum gravity is developed and the conditions for the existence of a local H-theorem or, alternatively, of a constant H-theorem are established.https://www.mdpi.com/1099-4300/21/4/418covariant quantum gravityGaussian solutionsBoltzmann–Shannon entropyH-theorem
collection DOAJ
language English
format Article
sources DOAJ
author Massimo Tessarotto
Claudio Cremaschini
spellingShingle Massimo Tessarotto
Claudio Cremaschini
Role of Quantum Entropy and Establishment of H-Theorems in the Presence of Graviton Sinks for Manifestly-Covariant Quantum Gravity
Entropy
covariant quantum gravity
Gaussian solutions
Boltzmann–Shannon entropy
H-theorem
author_facet Massimo Tessarotto
Claudio Cremaschini
author_sort Massimo Tessarotto
title Role of Quantum Entropy and Establishment of H-Theorems in the Presence of Graviton Sinks for Manifestly-Covariant Quantum Gravity
title_short Role of Quantum Entropy and Establishment of H-Theorems in the Presence of Graviton Sinks for Manifestly-Covariant Quantum Gravity
title_full Role of Quantum Entropy and Establishment of H-Theorems in the Presence of Graviton Sinks for Manifestly-Covariant Quantum Gravity
title_fullStr Role of Quantum Entropy and Establishment of H-Theorems in the Presence of Graviton Sinks for Manifestly-Covariant Quantum Gravity
title_full_unstemmed Role of Quantum Entropy and Establishment of H-Theorems in the Presence of Graviton Sinks for Manifestly-Covariant Quantum Gravity
title_sort role of quantum entropy and establishment of h-theorems in the presence of graviton sinks for manifestly-covariant quantum gravity
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2019-04-01
description Based on the introduction of a suitable quantum functional, identified here with the Boltzmann–Shannon entropy, entropic properties of the quantum gravitational field are investigated in the framework of manifestly-covariant quantum gravity theory. In particular, focus is given to gravitational quantum states in a background de Sitter space-time, with the addition of possible quantum non-unitarity effects modeled in terms of an effective quantum graviton sink localized near the de Sitter event horizon. The theory of manifestly-covariant quantum gravity developed accordingly is shown to retain its emergent-gravity features, which are recovered when the generalized-Lagrangian-path formalism is adopted, yielding a stochastic trajectory-based representation of the quantum wave equation. This permits the analytic determination of the quantum probability density function associated with the quantum gravity state, represented in terms of a generally dynamically-evolving shifted Gaussian function. As an application, the study of the entropic properties of quantum gravity is developed and the conditions for the existence of a local H-theorem or, alternatively, of a constant H-theorem are established.
topic covariant quantum gravity
Gaussian solutions
Boltzmann–Shannon entropy
H-theorem
url https://www.mdpi.com/1099-4300/21/4/418
work_keys_str_mv AT massimotessarotto roleofquantumentropyandestablishmentofhtheoremsinthepresenceofgravitonsinksformanifestlycovariantquantumgravity
AT claudiocremaschini roleofquantumentropyandestablishmentofhtheoremsinthepresenceofgravitonsinksformanifestlycovariantquantumgravity
_version_ 1725899581371187200