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Entropy
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Entropy in Covariant Quantum Gravity
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Entropy in Covariant Quantum Gravity

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (31 December 2019) | Viewed by 6057

Special Issue Editor

Prof. Dr. Massimo Tessarotto

E-Mail Website
Guest Editor
Department of Mathematics and Geosciences, University of Trieste, 34100 Trieste, Italy
Interests: quantum mechanics; general relativity; quantum field theory; special and general relativity; turbulence modeling; theoretical physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The notion of entropy, and particularly of statistical entropy, arises in many areas of physics, being related to the property of macroscopic irreversibility possibly arising in the finite/asymptotic behavior of dynamical systems, both classical and quantum. Although its role originates from thermodynamics and classical statistical mechanics (CSM) the concept of entropy has been greatly extended and now includes quantum gravity (QG).

In this Special Issue progress will be reported in the theory of quantum gravity, with particular reference to its covariant and manifestly-covariant realizations, which may actually help achieve insight into the possible role of quantum entropy. In this context, the latter is expected to be identified, in analogy to CSM, with a suitable Boltzmann-Shannon statistical entropy associated with the relevant quantum probability density function (PDF) which is characteristic of theory. Thus, generally it should correspond to the occurrence of non-stationary (in some suitable sense) quantum states. Specifically, to this end, consideration will be given to recent developments of QG that concern the adoption of either covariant or manifestly-covariant canonical approaches for the quantization of the space-time metric tensor. In both cases, the quantum PDF and the same quantum entropy can (or must) always be prescribed in terms of suitable $4-$scalars, with the second one being associated with an appropriate quantum expectation value of the same quantum PDF. For this purpose, review articles, as well as original research works, will be presented. Emphasis will be devoted in particular to a number of difficult/unsolved related issues, including:

  • The explicit construction of the quantum entropy in vacuum together with its corresponding entropy production;
  • The extension of the theory to include the treatment of event horizons as well either internal or external domains of black holes and the corresponding event horizons;
  • The investigation of the asymptotic behavior of the quantum entropy and, correspondingly, the possible validity, in analogy to non-relativistic quantum mechanics, of an asymptotic and/or local constant H-theorem;
  • The role of the cosmological constant in the determination of the quantum entropy and the related issue of the physical origin of the same cosmological constant.
Prof. Massimo Tessarotto

Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Quantum gravity
  • Covariant and manifestly covariant theories
  • Non-stationary quantum states
  • Asymptotic behavior
  • Quantum probability density function
  • Quantum entropy
  • Local/asymptotic H-theorems
  • Event horizons
  • Cosmological constant

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Published Papers (2 papers)

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Research

31 pages, 2421 KiB  
Article
Constraining LQG Graph with Light Surfaces: Properties of BH Thermodynamics for Mini-Super-Space, Semi-Classical Polymeric BH
by Daniela Pugliese and Giovanni Montani
Entropy 2020, 22(4), 402; https://doi.org/10.3390/e22040402 - 31 Mar 2020
Cited by 11 | Viewed by 2595
Abstract
This work participates in the research for potential areas of observational evidence of quantum effects on geometry in a black hole astrophysical context. We consider properties of a family of loop quantum corrected regular black hole (BHs) solutions and their horizons, focusing on [...] Read more.
This work participates in the research for potential areas of observational evidence of quantum effects on geometry in a black hole astrophysical context. We consider properties of a family of loop quantum corrected regular black hole (BHs) solutions and their horizons, focusing on the geometry symmetries. We study here a recently developed model, where the geometry is determined by a metric quantum modification outside the horizon. This is a regular static spherical solution of mini-super-space BH metric with Loop Quantum Gravity (LQG) corrections. The solutions are characterized delineating certain polymeric functions on the basis of the properties of the horizons and the emergence of a singularity in the limiting case of the Schwarzschild geometry. We discuss particular metric solutions on the base of the parameters of the polymeric model related to similar properties of structures, the metric Killing bundles (or metric bundles MBs), related to the BH horizons’ properties. A comparison with the Reissner–Norström geometry and the Kerr geometry with which analogies exist from the point of their respective MBs properties is done. The analysis provides a way to recognize these geometries and detect their main distinctive phenomenological evidence of LQG origin on the basis of the detection of stationary/static observers and the properties of light-like orbits within the analysis of the (conformal invariant) MBs related to the (local) causal structure. This approach could be applied in other quantum corrected BH solutions, constraining the characteristics of the underlining LQG-graph, as the minimal loop area, through the analysis of the null-like orbits and photons detection. The study of light surfaces associated with a diversified and wide range of BH phenomenology and grounding MBs definition provides a channel to search for possible astrophysical evidence. The main BHs thermodynamic characteristics are studied as luminosity, surface gravity, and temperature. Ultimately, the application of this method to this spherically symmetric approximate solution provides us with a way to clarify some formal aspects of MBs, in the presence of static, spherical symmetric spacetimes. Full article
(This article belongs to the Special Issue Entropy in Covariant Quantum Gravity)
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25 pages, 332 KiB  
Article
Role of Quantum Entropy and Establishment of H-Theorems in the Presence of Graviton Sinks for Manifestly-Covariant Quantum Gravity
by Massimo Tessarotto and Claudio Cremaschini
Entropy 2019, 21(4), 418; https://doi.org/10.3390/e21040418 - 19 Apr 2019
Cited by 7 | Viewed by 3031
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Entropy in Covariant Quantum Gravity)
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