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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: closed (31 October 2019) | Viewed by 20058

Special Issue Editor

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

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Keywords

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

Published Papers (5 papers)

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Research

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13 pages, 448 KiB  
Article
Nonlinear Fokker–Planck Equation Approach to Systems of Interacting Particles: Thermostatistical Features Related to the Range of the Interactions
by Angel R. Plastino and Roseli S. Wedemann
Entropy 2020, 22(2), 163; https://doi.org/10.3390/e22020163 - 31 Jan 2020
Cited by 8 | Viewed by 2817
Abstract
Nonlinear Fokker–Planck equations (NLFPEs) constitute useful effective descriptions of some interacting many-body systems. Important instances of these nonlinear evolution equations are closely related to the thermostatistics based on the S q power-law entropic functionals. Most applications of the connection between the NLFPE and [...] Read more.
Nonlinear Fokker–Planck equations (NLFPEs) constitute useful effective descriptions of some interacting many-body systems. Important instances of these nonlinear evolution equations are closely related to the thermostatistics based on the S q power-law entropic functionals. Most applications of the connection between the NLFPE and the S q 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, such as those corresponding to Newtonian gravitation. In particular, we consider a system of particles interacting via forces following the inverse square law and performing overdamped motion, that is described by a density obeying an integro-differential evolution equation that admits exact time-dependent solutions of the q-Gaussian form. These q-Gaussian solutions, which constitute a signature of S q -thermostatistics, evolve in a similar but not identical way to the solutions of an appropriate nonlinear, power-law Fokker–Planck equation. Full article
(This article belongs to the Special Issue Entropy and Gravitation)
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8 pages, 268 KiB  
Article
Statistical Mechanics-Based Schrödinger Treatment of Gravity
by Angelo Plastino and M. C. Rocca
Entropy 2019, 21(7), 682; https://doi.org/10.3390/e21070682 - 12 Jul 2019
Cited by 3 | Viewed by 2627
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 [...] 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

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8 pages, 253 KiB  
Review
Black Hole Entropy: A Closer Look
by Constantino Tsallis
Entropy 2020, 22(1), 17; https://doi.org/10.3390/e22010017 - 22 Dec 2019
Cited by 30 | Viewed by 8471
Abstract
In many papers in the literature, author(s) express their perplexity concerning the fact that the ( 3 + 1 ) black-hole ‘thermodynamical’ entropy appears to be proportional to its area and not to its volume, and would therefore seemingly be nonextensive, or, to [...] Read more.
In many papers in the literature, author(s) express their perplexity concerning the fact that the ( 3 + 1 ) black-hole ‘thermodynamical’ entropy appears to be proportional to its area and not to its volume, and would therefore seemingly be nonextensive, or, to be more precise, subextensive. To discuss this question on more clear terms, a non-Boltzmannian entropic functional noted S δ was applied [Tsallis and Cirto, Eur. Phys. J. C 73, 2487 (2013)] to this complex system which exhibits the so-called area-law. However, some nontrivial physical points still remain open, which we revisit now. This discussion is also 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. Full article
(This article belongs to the Special Issue Entropy and Gravitation)
15 pages, 337 KiB  
Review
Entropy and Gravitation—From Black Hole Computers to Dark Energy and Dark Matter
by Y. Jack Ng
Entropy 2019, 21(11), 1035; https://doi.org/10.3390/e21111035 - 25 Oct 2019
Cited by 7 | Viewed by 3188
Abstract
We show that the concept of entropy and the dynamics of gravitation provide the linchpin in a unified scheme to understand the physics of black hole computers, spacetime foam, dark energy, dark matter and the phenomenon of turbulence. We use three different methods [...] Read more.
We show that the concept of entropy and the dynamics of gravitation provide the linchpin in a unified scheme to understand the physics of black hole computers, spacetime foam, dark energy, dark matter and the phenomenon of turbulence. We use three different methods to estimate the foaminess of spacetime, which, in turn, provides a back-door way to derive the Bekenstein-Hawking formula for black hole entropy and the holographic principle. Generalizing the discussion for a static spacetime region to the cosmos, we find a component of dark energy (resembling an effective positive cosmological constant of the correct magnitude) in the current epoch of the universe. The conjunction of entropy and gravitation is shown to give rise to a phenomenological model of dark matter, revealing the natural emergence, in galactic and cluster dynamics, of a critical acceleration parameter related to the cosmological constant; the resulting mass profiles are consistent with observations. Unlike ordinary matter, the quanta of the dark sector are shown to obey infinite statistics. This property of dark matter may lead to some non-particle phenomenology and may explain why dark matter particles have not been detected in dark matter search experiments. We also show that there are deep similarities between the problem of “quantum gravity” (more specifically, the holographic spacetime foam) and turbulence. Full article
(This article belongs to the Special Issue Entropy and Gravitation)
17 pages, 329 KiB  
Review
A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation
by Flavia Pennini, Angel Plastino, Mario Rocca and Gustavo Ferri
Entropy 2019, 21(7), 677; https://doi.org/10.3390/e21070677 - 11 Jul 2019
Cited by 4 | Viewed by 2337
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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