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Special Issue "Entropy and Gravitation"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Astrophysics, Cosmology, and Black Holes".

Deadline for manuscript submissions: 31 October 2019.

Special Issue Editor

Guest Editor
Prof. Dr. Angelo Plastino

Physics Department, National University La Plata C.C.727, 1900 La Plata, Argentina
Website | E-Mail
Interests: Foundations of Quantum Mechanics; Quantum Information: Communication, Cryptography, and Computation; Quantum Optics and Metrology; Fundamental questions of Quantum Gravity, Cosmology, and Field Theory

Special Issue Information

Dear Colleagues,

It is a quite exciting, almost revolutionary question to ask ourselves whether gravity is fundamental or emergent.

A deep discussion on this issue might provide important links to a complete theory of quantum gravity, as a maximal aspiration, or will at least lead to interesting insights.

A notable example of such an insight into the nature of gravity arises from the analysis of black hole thermodynamics, which motivates general and putative connections between gravity and thermodynamics [1–4]. On this basis, Jacobson argued that the Einstein equation could be derived from the proportionality of entropy and the horizon area, together with the first law of thermodynamics. He considered the possibility that the Einstein equation might be regarded as a thermodynamic equation of state [5]. Later, Padmanabhan demonstrated that motion equations for gravity in any diffeomorphism invariant theory can be given a thermodynamic interpretation, closely connected to the structure of functional action [6,7].

These results suggest that gravity may be explained as an emergent phenomenon and might possess a thermodynamic or entropic origin [8]. In 2011, Verlinde introduced a novel argument for emergent gravity, based on the celebrated holographic principle [9].

Verlinde developed a convincing line of reasoning that purports to claim that gravity is not an elementary but an entropic force, which is caused by a change in the amount of information associated to the spatial positions of pieces of matter. This notion is exciting. If it is right, it might have important implications for the origin of gravity and its desired unification with the quantum realm. Verlinde’s conjecture [9] has actually been proven in a classical scenario [10].

The stage seems to be set for a Special Issue of Entropy that may provide didactic reviews on these issues as well as new, relevant proposals.

References

  1. Bardeen, J.M.; Carter, B.; Hawking, S.W. The four laws of black hole mechanics. Math. Phys. 1973, 31, 161–170.
  2. Bekenstein, J.D. Extraction of energy and charge from a black hole. Rev. D 1973, 7, 949–953.
  3. Bekenstein, J.D. Black holes and entropy. Rev. D 1973, 7, 2333–2346.
  4. Hawking, S.W. Particle creation by black holes. Math. Phys. 1975, 43, 199–220.
  5. Jacobson, T. Thermodynamics of spacetime: The Einstein equation of state. Rev. Lett. 1995, 75, 1260–1263.
  6. Padmanabhan, T. Entropy density of spacetime and thermodynamic interpretation of field equations of gravity in any diffeomorphism invariant theory. arXiv 2009, arXiv:0903.1254.
  7. Padmanabhan, T. Entropy density of spacetime and gravity: A conceptual synthesis. J. Mod. Phys. D 2009, 18, 2189–2193.
  8. Padmanabhan, T. Thermodynamical aspects of gravity: New insights. arXiv 2009, arXiv:0911.5004.
  9. Verlinde, E.P. On the origin of gravity and the laws of Newton. arXiv 2010, arXiv:1001.0785.
  10. Plastino, A.; Rocca, M.C. On the entropic derivation of the r -2 Newtonian gravity force. Physica A 2018, 505, 190–195.

Prof. Angelo Plastino
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 papers will be 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 1600 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

  • Gravitation
  • Entropic measures
  • Non-linear mean-field theories
  • Black holes
  • Verlinde’s conjecture

Published Papers (2 papers)

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Research

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Open AccessFeature PaperArticle
Statistical Mechanics-Based Schrödinger Treatment of Gravity
Entropy 2019, 21(7), 682; https://doi.org/10.3390/e21070682
Received: 22 April 2019 / Revised: 21 June 2019 / Accepted: 9 July 2019 / Published: 12 July 2019
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Abstract
The entropic gravity conception proposes that what has been traditionally interpreted as unobserved dark matter might be merely the product of quantum effects. These effects would produce a novel sort of positive energy that translates into dark matter via E=mc [...] Read more.
The entropic gravity conception proposes that what has been traditionally interpreted as unobserved dark matter might be merely the product of quantum effects. These effects would produce a novel sort of positive energy that translates into dark matter via E = m c 2 . In the case of axions, this perspective has been shown to yield quite sensible, encouraging results [DOI:10.13140/RG.2.2.17894.88641]. Therein, a simple Schrödinger mechanism was utilized, in which his celebrated equation is solved with a potential function based on the microscopic Verlinde’s entropic force advanced in [Physica A 511 (2018) 139]. In this paper, we revisit this technique with regards to fermions’ behavior (specifically, baryons). Full article
(This article belongs to the Special Issue Entropy and Gravitation)
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Review

Jump to: Research

Open AccessReview
A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation
Entropy 2019, 21(7), 677; https://doi.org/10.3390/e21070677
Received: 9 May 2019 / Revised: 5 July 2019 / Accepted: 8 July 2019 / Published: 11 July 2019
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Abstract
It is common lore that the canonical gravitational partition function Z associated with the classical Boltzmann-Gibbs (BG) exponential distribution cannot be built up because of mathematical pitfalls. The integral needed for writing up Z diverges. We review here how to avoid this pitfall [...] Read more.
It is common lore that the canonical gravitational partition function Z associated with the classical Boltzmann-Gibbs (BG) exponential distribution cannot be built up because of mathematical pitfalls. The integral needed for writing up Z diverges. We review here how to avoid this pitfall and obtain a (classical) statistical mechanics of Newton’s gravitation. This is done using (1) the analytical extension treatment obtained of Gradshteyn and Rizhik and (2) the well known dimensional regularization technique. Full article
(This article belongs to the Special Issue Entropy and Gravitation)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Black hole entropy: a closer look
Author: Constantino Tsallis
Abstract: In many papers in the literature we can read the author(s) perplexity concerning the fact that the black hole thermodynamical entropy is proportional to its area and not to its volume, and would therefore seemingly be nonextensive — subextensive to be more precise —. To discuss this question on more clear terms, a non-Boltzmannian entropic functional noted S_delta was applied [Tsallis and Cirto, Eur. Phys. J. C 73, 2487 (2013)]  to this complex system which exhibits a so-called area-law. However, some nontrivial physical points still remain open, which we revisit now. This discussion is based on the fact that the well known Bekenstein-Hawking entropy can be expressed as being proportional to the event horizon area divided by the square of the Planck length.

Title: Nonlinear Fokker-Planck Equation Approach to Systems of Interacting Particles: Thermodynamical Features Related to the Range of the Interactions
Author: A.R. Plastino
Abstract: The application of nonlinear Fokker-Planck equations (NLFPE) to the study of interacting many-body systems has attracted considerable attention recently. Important instances of these nonlinear evolution equations are closely related to the thermostatistics based on the Sq power-law entropic functionals. Most applications of this connection between the NLFPE and the Sq entropies have focused on systems interacting through short-range forces. In the present contribution we re-visit the NLFPE approach to interacting systems, in order to clarify the role played by the range of the interactions, and to explore the possibility of developing similar treatments for systems with long-range interactions, including particular instances of self-gravitating systems.
Keywords: Nonlinear Fokker-Planck Equation, Nonadditive Entropies, Long Range Interactions, Gravitation

Title: Classical Statistical Mechanics' treatment of Gravitation
Author: F. Pennini, A. Plastino, M. C. Rocca
Abstract: It is believed that the canonical gravitational partition function Z associated to the classical Boltzmann-Gibbs (BG) distribution e^(−βH)/Z cannot be constructed because the integral needed for building up Z includes an exponential and thus diverges at the origin. In this review we discuss how, by recourse to 1) the analytical extension treatment obtained for the first time ever by Gradshteyn and Rizhik, via an appropriate formula for such case and 2) the dimensional regularization approach of Bollini and Giambiagi's, one can indeed obtain finite gravitational results employing the BG distribution. Our considerations are then applied to Tsallis' classical statistical mechanics. We continue the discussion by tackling the special relativity treatment both in the BG and Tsallis environments. Our main conclusion will be that of providing a finite partition function for the two-body gravitational problem in various circumstances.
Keywords: Boltzmann-Gibbs distribution, Tsallis distribution, gravitation potential, divergences, dimensional regularization, specific heat

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