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Entropy
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Statistical Mechanics of Self-Gravitating Systems
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Statistical Mechanics of Self-Gravitating Systems

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 (15 March 2024) | Viewed by 2455

Special Issue Editor

Prof. Dr. Bruce N. Miller

E-Mail Website
Guest Editor
Department of Physics and Astronomy, Texas Christian University, Fort Worth, TX 76129, USA
Interests: statistical physics and nonlinear dynamics of gravity using one-dimensional models: evolution, relaxation, diffusion, phase transitions, fractal properties and cosmology; low-dimensional nonlinear dynamics: new mechanisms (beyond KAM) for generating chaos; quantum localization of a low-mass particles: applications to positron and positronium annihilation in fluids

Special Issue Information

Dear Colleagues,

Although the gravitational force is very weak, observational astronomy provides us with numerous examples of assembled systems where it is the central unifying element. Going down in scale, galactic clusters, galaxies, globular clusters and solar systems come to mind, but there are other examples as well. At first glance, it would be natural to suppose that statistical mechanics should provide a unifying set of principles for understanding the main properties of these systems. However, the infinite range and short-range singularity of the Newtonian gravitational force introduces challenges for the standard theories that have yet to be fully resolved. Since they lack the short-range singularity, one-dimensional gravitational models are more susceptible to standard treatments and have had some success in providing insights into their 3D cousins. For example, about fifty years ago Rybicki was able to analytically formulate the equilibrium statistical mechanics of an open 1D gravitational system on the line in both the canonical and microcanonical ensembles. However, challenges remain even in that domain. Researchers have employed non-standard statistical mechanics to approach these issues for 3D, but a clear systematic theory has yet to be achieved. Perhaps we are now in a better position to address them, or at least take stock of what can be achieved and where further progress can be made.

Prof. Dr. Bruce N. Miller
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.

Published Papers (3 papers)

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Research

11 pages, 430 KiB  
Article
Revisiting the Surface Brightness Profile of the Stellar Disk with the Statistical Mechanics of the Self-Gravitating System with the Central Body
by Dong-Biao Kang
Entropy 2024, 26(4), 297; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040297 - 28 Mar 2024
Viewed by 446
Abstract
We have explored the exponential surface brightness profile (SBP) of stellar disks, a topic extensively discussed by many authors yet seldom integrated with the study of correlations between black holes, bulges, and entire disks. Building upon our prior work in the statistical mechanics [...] Read more.
We have explored the exponential surface brightness profile (SBP) of stellar disks, a topic extensively discussed by many authors yet seldom integrated with the study of correlations between black holes, bulges, and entire disks. Building upon our prior work in the statistical mechanics of disk-shaped systems and aligning with methodologies from other research, we analyze the influence of the central body. This analysis reveals analytical relationships among black holes, bulges, and the entire stellar disk. Additionally, we incorporate a specific angular momentum distribution (SAMD) that aligns more closely with observational data, showing that for the self-gravitating disk, with the same surface density, a reduction in its spin results in only a slight decrease in its radius, whereas with the same SAMD, an increment in its spin significantly limits its extent. A key feature of our model is its prediction that the surface density profile of an isolated disk will invariably exhibit downbending at a sufficient distance, a hypothesis that future observations can test. Our refined equations provide a notably improved fit for SBPs, particularly in the central regions of stellar disks. While our findings underscore the significance of statistical mechanics in comprehending spiral galaxy structures, they also highlight areas in our approach that warrant further discussion and exploration. Full article
(This article belongs to the Special Issue Statistical Mechanics of Self-Gravitating Systems)
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10 pages, 325 KiB  
Article
Analysis of Self-Gravitating Fluid Instabilities from the Post-Newtonian Boltzmann Equation
by Gilberto M. Kremer
Entropy 2024, 26(3), 246; https://0-doi-org.brum.beds.ac.uk/10.3390/e26030246 - 10 Mar 2024
Viewed by 732
Abstract
Self-gravitating fluid instabilities are analysed within the framework of a post-Newtonian Boltzmann equation coupled with the Poisson equations for the gravitational potentials of the post-Newtonian theory. The Poisson equations are determined from the knowledge of the energy–momentum tensor calculated from a post-Newtonian Maxwell–Jüttner [...] Read more.
Self-gravitating fluid instabilities are analysed within the framework of a post-Newtonian Boltzmann equation coupled with the Poisson equations for the gravitational potentials of the post-Newtonian theory. The Poisson equations are determined from the knowledge of the energy–momentum tensor calculated from a post-Newtonian Maxwell–Jüttner distribution function. The one-particle distribution function and the gravitational potentials are perturbed from their background states, and the perturbations are represented by plane waves characterised by a wave number vector and time-dependent small amplitudes. The time-dependent amplitude of the one-particle distribution function is supposed to be a linear combination of the summational invariants of the post-Newtonian kinetic theory. From the coupled system of differential equations for the time-dependent amplitudes of the one-particle distribution function and gravitational potentials, an evolution equation for the mass density contrast is obtained. It is shown that for perturbation wavelengths smaller than the Jeans wavelength, the mass density contrast propagates as harmonic waves in time. For perturbation wavelengths greater than the Jeans wavelength, the mass density contrast grows in time, and the instability growth in the post-Newtonian theory is more accentuated than the one of the Newtonian theory. Full article
(This article belongs to the Special Issue Statistical Mechanics of Self-Gravitating Systems)
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15 pages, 3243 KiB  
Article
A Monte Carlo Method for Calculating Lynden-Bell Equilibrium in Self-Gravitating Systems
by Tarcísio N. Teles, Calvin A. F. Farias, Renato Pakter and Yan Levin
Entropy 2023, 25(10), 1379; https://0-doi-org.brum.beds.ac.uk/10.3390/e25101379 - 25 Sep 2023
Viewed by 748
Abstract
We present a Monte Carlo approach that allows us to easily implement Lynden-Bell (LB) entropy maximization for an arbitrary initial particle distribution. The direct maximization of LB entropy for an arbitrary initial distribution requires an infinite number of Lagrange multipliers to account for [...] Read more.
We present a Monte Carlo approach that allows us to easily implement Lynden-Bell (LB) entropy maximization for an arbitrary initial particle distribution. The direct maximization of LB entropy for an arbitrary initial distribution requires an infinite number of Lagrange multipliers to account for the Casimir invariants. This has restricted studies of Lynden-Bell’s violent relaxation theory to only a very small class of initial conditions of a very simple waterbag form, for which the entropy maximization can be performed numerically. In the present approach, an arbitrary initial distribution is discretized into density levels which are then evolved using an efficient Monte Carlo algorithm towards the final equilibrium state. A comparison is also made between the LB equilibrium and explicit Molecular Dynamics simulations. We find that for most initial distributions, relaxation is incomplete and the system is not able to reach the state of maximum LB entropy. In particular, we see that the tail of the stationary particle distribution is very different from the one predicted by the theory of violent relaxation, with a hard cutoff instead of an algebraic decay predicted by LB’s theory. Full article
(This article belongs to the Special Issue Statistical Mechanics of Self-Gravitating Systems)
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