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Geometry in Thermodynamics II
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Geometry in Thermodynamics II

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

Deadline for manuscript submissions: closed (28 February 2018) | Viewed by 33432

Special Issue Editor

Prof. Dr. George Ruppeiner

E-Mail Website
Guest Editor
Division of Natural Sciences, New College of Florida, 5800 Bay Shore Road, Sarasota, FL 34243, USA
Interests: metric geometry in thermodynamics; fluid behavior; metastable liquid water; solid-like fluid properties; magnetic spin models; black holes; thermodynamic curvature; critical phenomena, and strongly interacting Fermi systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We reopen the call for submissions of manuscripts to the volume "Geometry in Thermodynamics." Our updated call is intended to accommodate a somewhat-expanded span of topics, new researchers in the field, as well as anyone else who would like to contribute at this point. We welcome articles on symplectic geometry, contact geometry, inner product geometry, metric geometry, information geometry, and Legendre invariant geometry. Applications can include finite-time thermodynamics, fluctuation phenomena, black hole thermodynamics, and phase transitions. In addition, we invite articles related to model evaluations, quantum phase transitions, stochastic thermodynamics, machine learning, control theory, computer vision, optimal transport theory, and Wasserstein geometry. Geometry of thermodynamics is a growing area of research, with many new contributions in a number of areas.

Prof. Dr. George Ruppeiner
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.

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Published Papers (7 papers)

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Research

22 pages, 1252 KiB  
Article
Thermodynamic Black Holes
by George Ruppeiner
Entropy 2018, 20(6), 460; https://doi.org/10.3390/e20060460 - 13 Jun 2018
Cited by 22 | Viewed by 4705
Abstract
Black holes pose great difficulties for theory since gravity and quantum theory must be combined in some as yet unknown way. An additional difficulty is that detailed black hole observational data to guide theorists is lacking. In this paper, I sidestep the difficulties [...] Read more.
Black holes pose great difficulties for theory since gravity and quantum theory must be combined in some as yet unknown way. An additional difficulty is that detailed black hole observational data to guide theorists is lacking. In this paper, I sidestep the difficulties of combining gravity and quantum theory by employing black hole thermodynamics augmented by ideas from the information geometry of thermodynamics. I propose a purely thermodynamic agenda for choosing correct candidate black hole thermodynamic scaled equations of state, parameterized by two exponents. These two adjustable exponents may be set to accommodate additional black hole information, either from astrophysical observations or from some microscopic theory, such as string theory. My approach assumes implicitly that the as yet unknown microscopic black hole constituents have strong effective interactions between them, of a type found in critical phenomena. In this picture, the details of the microscopic interaction forces are not important, and the essential macroscopic picture emerges from general assumptions about the number of independent thermodynamic variables, types of critical points, boundary conditions, and analyticity. I use the simple Kerr and Reissner-Nordström black holes for guidance, and find candidate equations of state that embody several the features of these purely gravitational models. My approach may offer a productive new way to select black hole thermodynamic equations of state representing both gravitational and quantum properties. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics II)
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7 pages, 247 KiB  
Article
On the Contact Geometry and the Poisson Geometry of the Ideal Gas
by J. M. Isidro and P. Fernández de Córdoba
Entropy 2018, 20(4), 247; https://doi.org/10.3390/e20040247 - 03 Apr 2018
Cited by 5 | Viewed by 2789
Abstract
We elaborate on existing notions of contact geometry and Poisson geometry as applied to the classical ideal gas. Specifically, we observe that it is possible to describe its dynamics using a 3-dimensional contact submanifold of the standard 5-dimensional contact manifold used in the [...] Read more.
We elaborate on existing notions of contact geometry and Poisson geometry as applied to the classical ideal gas. Specifically, we observe that it is possible to describe its dynamics using a 3-dimensional contact submanifold of the standard 5-dimensional contact manifold used in the literature. This reflects the fact that the internal energy of the ideal gas depends exclusively on its temperature. We also present a Poisson algebra of thermodynamic operators for a quantum-like description of the classical ideal gas. The central element of this Poisson algebra is proportional to Boltzmann’s constant. A Hilbert space of states is identified and a system of wave equations governing the wavefunction is found. Expectation values for the operators representing pressure, volume and temperature are found to satisfy the classical equations of state. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics II)
10 pages, 263 KiB  
Article
Thermodynamic Properties of a Regular Black Hole in Gravity Coupling to Nonlinear Electrodynamics
by Yi-Huan Wei
Entropy 2018, 20(3), 192; https://doi.org/10.3390/e20030192 - 13 Mar 2018
Cited by 8 | Viewed by 3500
Abstract
We first calculate the heat capacities of the nonlinear electrodynamics (NED) black hole for fixed mass and electric charge, and the electric capacitances for fixed mass and entropy. Then, we study the properties of the Ruppeiner thermodynamic geometry of the NED black hole. [...] Read more.
We first calculate the heat capacities of the nonlinear electrodynamics (NED) black hole for fixed mass and electric charge, and the electric capacitances for fixed mass and entropy. Then, we study the properties of the Ruppeiner thermodynamic geometry of the NED black hole. Lastly, some discussions on the thermal stability of the NED black hole and the implication to the flatness of its Ruppeiner thermodynamic geometry are given. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics II)
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3538 KiB  
Article
Understanding the Fractal Dimensions of Urban Forms through Spatial Entropy
by Yanguang Chen, Jiejing Wang and Jian Feng
Entropy 2017, 19(11), 600; https://doi.org/10.3390/e19110600 - 09 Nov 2017
Cited by 47 | Viewed by 7930
Abstract
The spatial patterns and processes of cities can be described with various entropy functions. However, spatial entropy always depends on the scale of measurement, and it is difficult to find a characteristic value for it. In contrast, fractal parameters can be employed to [...] Read more.
The spatial patterns and processes of cities can be described with various entropy functions. However, spatial entropy always depends on the scale of measurement, and it is difficult to find a characteristic value for it. In contrast, fractal parameters can be employed to characterize scale-free phenomena and reflect the local features of random multi-scaling structure. This paper is devoted to exploring the similarities and differences between spatial entropy and fractal dimension in urban description. Drawing an analogy between cities and growing fractals, we illustrate the definitions of fractal dimension based on different entropy concepts. Three representative fractal dimensions in the multifractal dimension set, capacity dimension, information dimension, and correlation dimension, are utilized to make empirical analyses of the urban form of two Chinese cities, Beijing and Hangzhou. The results show that the entropy values vary with the measurement scale, but the fractal dimension value is stable is method and study area are fixed; if the linear size of boxes is small enough (e.g., <1/25), the linear correlation between entropy and fractal dimension is significant (based on the confidence level of 99%). Further empirical analysis indicates that fractal dimension is close to the characteristic values of spatial entropy. This suggests that the physical meaning of fractal dimension can be interpreted by the ideas from entropy and scaling and the conclusion is revealing for future spatial analysis of cities. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics II)
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492 KiB  
Article
Radially Excited AdS5 Black Holes in Einstein–Maxwell–Chern–Simons Theory
by Jose Luis Blázquez-Salcedo
Entropy 2017, 19(10), 567; https://doi.org/10.3390/e19100567 - 24 Oct 2017
Viewed by 3770
Abstract
In the large coupling regime of the 5-dimensional Einstein–Maxwell–Chern–Simons theory, charged and rotating cohomogeneity-1 black holes form sequences of extremal and non-extremal radially excited configurations. These asymptotically global Anti-de Sitter (AdS 5 ) black holes form a discrete set of solutions, characterised by [...] Read more.
In the large coupling regime of the 5-dimensional Einstein–Maxwell–Chern–Simons theory, charged and rotating cohomogeneity-1 black holes form sequences of extremal and non-extremal radially excited configurations. These asymptotically global Anti-de Sitter (AdS 5 ) black holes form a discrete set of solutions, characterised by the vanishing of the total angular momenta, or the horizon angular velocity. However, the solutions are not static. In this paper, we study the branch structure that contains these excited states, and its relation with the static Reissner–Nordström-AdS black hole. Thermodynamic properties of these solutions are considered, revealing that the branches with lower excitation number can become thermodynamically unstable beyond certain critical solutions that depend on the free parameters of the configuration. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics II)
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239 KiB  
Article
Contact Hamiltonian Dynamics: The Concept and Its Use
by Alessandro Bravetti
Entropy 2017, 19(10), 535; https://doi.org/10.3390/e19100535 - 11 Oct 2017
Cited by 79 | Viewed by 5960
Abstract
We give a short survey on the concept of contact Hamiltonian dynamics and its use in several areas of physics, namely reversible and irreversible thermodynamics, statistical physics and classical mechanics. Some relevant examples are provided along the way. We conclude by giving insights [...] Read more.
We give a short survey on the concept of contact Hamiltonian dynamics and its use in several areas of physics, namely reversible and irreversible thermodynamics, statistical physics and classical mechanics. Some relevant examples are provided along the way. We conclude by giving insights into possible future directions. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics II)
282 KiB  
Article
The Legendre Transform in Non-Additive Thermodynamics and Complexity
by Nikolaos Kalogeropoulos
Entropy 2017, 19(7), 298; https://doi.org/10.3390/e19070298 - 23 Jun 2017
Cited by 4 | Viewed by 4126
Abstract
We present an argument which purports to show that the use of the standard Legendre transform in non-additive Statistical Mechanics is not appropriate. For concreteness, we use as paradigm, the case of systems which are conjecturally described by the (non-additive) Tsallis entropy. We [...] Read more.
We present an argument which purports to show that the use of the standard Legendre transform in non-additive Statistical Mechanics is not appropriate. For concreteness, we use as paradigm, the case of systems which are conjecturally described by the (non-additive) Tsallis entropy. We point out the form of the modified Legendre transform that should be used, instead, in the non-additive thermodynamics induced by the Tsallis entropy. We comment on more general implications of this proposal for the thermodynamics of “complex systems”. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics II)
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