E-Mail Alert

Add your e-mail address to receive forthcoming issues of this journal:

Journal Browser

Journal Browser

Special Issue "Geometry in Thermodynamics"

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

Deadline for manuscript submissions: closed (30 June 2015)

Special Issue Editor

Guest Editor
Prof. Dr. George Ruppeiner

New College of Florida, Division of Natural Sciences, 5800 Bay Shore Road, Sarasota, FL 34243-2109, USA
Website | E-Mail
Phone: 941-487-4388
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 Issue Information

Dear Colleagues,

Some time ago, thermodynamics gained a reputation of being complete, both in its statement of concepts, and in the scope of its application. Yet a number of geometrical approaches have brought new ideas to the field. The aim of this Special Issue on geometry in thermodynamics is to bring a broad range of such ideas together including, but are not restricted to: 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, first and second-order phase transitions, and critical points.

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 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 1500 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

  • thermodynamic metric geometry
  • black hole thermodynamics
  • thermodynamic inner product geometry
  • finite-time thermodynamics
  • fluctuations
  • Legendre invariant geometry
  • thermodynamic curvature
  • symplectic geometry

Related Special Issue

Published Papers (9 papers)

View options order results:
result details:
Displaying articles 1-9
Export citation of selected articles as:

Research

Jump to: Review

Open AccessArticle Dualistic Hessian Structures Among the Thermodynamic Potentials in the κ-Thermostatistics
Entropy 2015, 17(10), 7213-7229; https://doi.org/10.3390/e17107213
Received: 28 July 2015 / Revised: 29 September 2015 / Accepted: 15 October 2015 / Published: 22 October 2015
Cited by 8 | PDF Full-text (260 KB) | HTML Full-text | XML Full-text
Abstract
We explore the information geometric structures among the thermodynamic potentials in the κ-thermostatistics, which is a generalized thermostatistics based on the κ-deformed entropy. We show that there exists two different kinds of dualistic Hessian structures: one is associated with the κ-escort expectations and
[...] Read more.
We explore the information geometric structures among the thermodynamic potentials in the κ-thermostatistics, which is a generalized thermostatistics based on the κ-deformed entropy. We show that there exists two different kinds of dualistic Hessian structures: one is associated with the κ-escort expectations and the other with the standard expectations. The associated κ-generalized metrics are derived and related to the κ-generalized fluctuation-response relations among the thermodynamic potentials in the κ-thermostatistics. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics)
Open AccessArticle Thermodynamic Metrics and Black Hole Physics
Entropy 2015, 17(9), 6503-6518; https://doi.org/10.3390/e17096503
Received: 16 July 2015 / Revised: 24 August 2015 / Accepted: 31 August 2015 / Published: 22 September 2015
Cited by 6 | PDF Full-text (314 KB) | HTML Full-text | XML Full-text
Abstract
We give a brief survey of thermodynamic metrics, in particular the Hessian of the entropy function, and how they apply to black hole thermodynamics. We then provide a detailed discussion of the Gibbs surface of Kerr black holes. In particular, we analyze its
[...] Read more.
We give a brief survey of thermodynamic metrics, in particular the Hessian of the entropy function, and how they apply to black hole thermodynamics. We then provide a detailed discussion of the Gibbs surface of Kerr black holes. In particular, we analyze its global properties and extend it to take the entropy of the inner horizon into account. A brief discussion of Kerr–Newman black holes is included. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics)
Figures

Figure 1

Open AccessArticle Entropies from Coarse-graining: Convex Polytopes vs. Ellipsoids
Entropy 2015, 17(9), 6329-6378; https://doi.org/10.3390/e17096329
Received: 16 July 2015 / Revised: 9 September 2015 / Accepted: 10 September 2015 / Published: 15 September 2015
Cited by 3 | PDF Full-text (393 KB) | HTML Full-text | XML Full-text
Abstract
We examine the Boltzmann/Gibbs/Shannon SBGS and the non-additive Havrda-Charvát/Daróczy/Cressie-Read/Tsallis Sq and the Kaniadakis κ-entropy Sκ from the viewpoint of coarse-graining, symplectic capacities and convexity. We argue that the functional form of such entropies can be ascribed to a discordance in phase-space coarse-graining between
[...] Read more.
We examine the Boltzmann/Gibbs/Shannon SBGS and the non-additive Havrda-Charvát/Daróczy/Cressie-Read/Tsallis Sq and the Kaniadakis κ-entropy Sκ from the viewpoint of coarse-graining, symplectic capacities and convexity. We argue that the functional form of such entropies can be ascribed to a discordance in phase-space coarse-graining between two generally different approaches: the Euclidean/Riemannian metric one that reflects independence and picks cubes as the fundamental cells in coarse-graining and the symplectic/canonical one that picks spheres/ellipsoids for this role. Our discussion is motivated by and confined to the behaviour of Hamiltonian systems of many degrees of freedom. We see that Dvoretzky’s theorem provides asymptotic estimates for the minimal dimension beyond which these two approaches are close to each other. We state and speculate about the role that dualities may play in this viewpoint. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics)
Open AccessArticle Metrics and Energy Landscapes in Irreversible Thermodynamics
Entropy 2015, 17(9), 6304-6317; https://doi.org/10.3390/e17096304
Received: 1 June 2015 / Revised: 12 August 2015 / Accepted: 1 September 2015 / Published: 10 September 2015
Cited by 3 | PDF Full-text (1012 KB) | HTML Full-text | XML Full-text
Abstract
We describe how several metrics are possible in thermodynamic state space but that only one, Weinhold’s, has achieved widespread use. Lengths calculated based on this metric have been used to bound dissipation in finite-time (irreversible) processes be they continuous or discrete, and described
[...] Read more.
We describe how several metrics are possible in thermodynamic state space but that only one, Weinhold’s, has achieved widespread use. Lengths calculated based on this metric have been used to bound dissipation in finite-time (irreversible) processes be they continuous or discrete, and described in the energy picture or the entropy picture. Examples are provided from thermodynamics of heat conversion processes as well as chemical reactions. Even losses in economics can be bounded using a thermodynamic type metric. An essential foundation for the metric is a complete equation of state including all extensive variables of the system; examples are given. Finally, the second law of thermodynamics imposes convexity on any equation of state, be it analytical or empirical. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics)
Figures

Figure 1

Open AccessArticle Conformal Gauge Transformations in Thermodynamics
Entropy 2015, 17(9), 6150-6168; https://doi.org/10.3390/e17096150
Received: 27 June 2015 / Revised: 25 August 2015 / Accepted: 28 August 2015 / Published: 2 September 2015
Cited by 6 | PDF Full-text (237 KB) | HTML Full-text | XML Full-text
Abstract
In this work, we show that the thermodynamic phase space is naturally endowed with a non-integrable connection, defined by all of those processes that annihilate the Gibbs one-form, i.e., reversible processes. We argue that such a connection is invariant under re-scalings of the
[...] Read more.
In this work, we show that the thermodynamic phase space is naturally endowed with a non-integrable connection, defined by all of those processes that annihilate the Gibbs one-form, i.e., reversible processes. We argue that such a connection is invariant under re-scalings of the connection one-form, whilst, as a consequence of the non-integrability of the connection, its curvature is not and, therefore, neither is the associated pseudo-Riemannian geometry. We claim that this is not surprising, since these two objects are associated with irreversible processes. Moreover, we provide the explicit form in which all of the elements of the geometric structure of the thermodynamic phase space change under a re-scaling of the connection one-form. We call this transformation of the geometric structure a conformal gauge transformation. As an example, we revisit the change of the thermodynamic representation and consider the resulting change between the two metrics on the thermodynamic phase space, which induce Weinhold’s energy metric and Ruppeiner’s entropy metric. As a by-product, we obtain a proof of the well-known conformal relation between Weinhold’s and Ruppeiner’s metrics along the equilibrium directions. Finally, we find interesting properties of the almost para-contact structure and of its eigenvectors, which may be of physical interest. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics)
Open AccessArticle Generalised Complex Geometry in Thermodynamical Fluctuation Theory
Entropy 2015, 17(8), 5888-5902; https://doi.org/10.3390/e17085888
Received: 29 May 2015 / Revised: 17 August 2015 / Accepted: 19 August 2015 / Published: 20 August 2015
Cited by 3 | PDF Full-text (221 KB) | HTML Full-text | XML Full-text
Abstract
We present a brief overview of some key concepts in the theory of generalized complex manifolds. This new geometry interpolates, so to speak, between symplectic geometry and complex geometry. As such it provides an ideal framework to analyze thermodynamical fluctuation theory in the
[...] Read more.
We present a brief overview of some key concepts in the theory of generalized complex manifolds. This new geometry interpolates, so to speak, between symplectic geometry and complex geometry. As such it provides an ideal framework to analyze thermodynamical fluctuation theory in the presence of gravitational fields. To illustrate the usefulness of generalized complex geometry, we examine a simplified version of the Unruh effect: the thermalising effect of gravitational fields on the Schroedinger wavefunction. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics)
Open AccessArticle Geometric Interpretation of Surface Tension Equilibrium in Superhydrophobic Systems
Entropy 2015, 17(7), 4684-4700; https://doi.org/10.3390/e17074684
Received: 18 June 2015 / Revised: 24 June 2015 / Accepted: 30 June 2015 / Published: 6 July 2015
Cited by 8 | PDF Full-text (1597 KB) | HTML Full-text | XML Full-text
Abstract
Surface tension and surface energy are closely related, although not identical concepts. Surface tension is a generalized force; unlike a conventional mechanical force, it is not applied to any particular body or point. Using this notion, we suggest a simple geometric interpretation of
[...] Read more.
Surface tension and surface energy are closely related, although not identical concepts. Surface tension is a generalized force; unlike a conventional mechanical force, it is not applied to any particular body or point. Using this notion, we suggest a simple geometric interpretation of the Young, Wenzel, Cassie, Antonoff and Girifalco–Good equations for the equilibrium during wetting. This approach extends the traditional concept of Neumann’s triangle. Substances are presented as points, while tensions are vectors connecting the points, and the equations and inequalities of wetting equilibrium obtain simple geometric meaning with the surface roughness effect interpreted as stretching of corresponding vectors; surface heterogeneity is their linear combination, and contact angle hysteresis is rotation. We discuss energy dissipation mechanisms during wetting due to contact angle hysteresis, the superhydrophobicity and the possible entropic nature of the surface tension. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics)
Open AccessArticle A Possible Cosmological Application of Some Thermodynamic Properties of the Black Body Radiation in n-Dimensional Euclidean Spaces
Entropy 2015, 17(7), 4563-4581; https://doi.org/10.3390/e17074563
Received: 18 March 2015 / Revised: 25 May 2015 / Accepted: 16 June 2015 / Published: 29 June 2015
Cited by 1 | PDF Full-text (1728 KB) | HTML Full-text | XML Full-text
Abstract
In this work, we present the generalization of some thermodynamic properties of the black body radiation (BBR) towards an n-dimensional Euclidean space. For this case, the Planck function and the Stefan–Boltzmann law have already been given by Landsberg and de Vos and some
[...] Read more.
In this work, we present the generalization of some thermodynamic properties of the black body radiation (BBR) towards an n-dimensional Euclidean space. For this case, the Planck function and the Stefan–Boltzmann law have already been given by Landsberg and de Vos and some adjustments by Menon and Agrawal. However, since then, not much more has been done on this subject, and we believe there are some relevant aspects yet to explore. In addition to the results previously found, we calculate the thermodynamic potentials, the efficiency of the Carnot engine, the law for adiabatic processes and the heat capacity at constant volume. There is a region at which an interesting behavior of the thermodynamic potentials arises: maxima and minima appear for the n—dimensional BBR system at very high temperatures and low dimensionality, suggesting a possible application to cosmology. Finally, we propose that an optimality criterion in a thermodynamic framework could be related to the 3—dimensional nature of the universe. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics)

Review

Jump to: Research

Open AccessReview Geometry of Multiscale Nonequilibrium Thermodynamics
Entropy 2015, 17(9), 5938-5964; https://doi.org/10.3390/e17095938
Received: 2 June 2015 / Revised: 14 August 2015 / Accepted: 20 August 2015 / Published: 25 August 2015
Cited by 7 | PDF Full-text (298 KB) | HTML Full-text | XML Full-text
Abstract
The time evolution of macroscopic systems can be experimentally observed and mathematically described on many different levels of description. It has been conjectured that the governing equations on all levels are particular realizations of a single abstract equation. We support this conjecture by
[...] Read more.
The time evolution of macroscopic systems can be experimentally observed and mathematically described on many different levels of description. It has been conjectured that the governing equations on all levels are particular realizations of a single abstract equation. We support this conjecture by interpreting the abstract equation as a geometrical formulation of general nonequilibrium thermodynamics. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics)
Back to Top