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Entropy
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Thermodynamics, Geometry and Control Theory
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Thermodynamics, Geometry and Control Theory

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

Deadline for manuscript submissions: closed (31 December 2020) | Viewed by 8247

Special Issue Editor

Prof. Dr. Valentin Lychagin

E-Mail Website
Guest Editor
1. Department of Mathematics and Statistics, The Arctic University of Norway, N-9037 Tromso, Norway
2. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 117997 Moscow, Russia
Interests: differential equations; symmetries; conservation laws; differential invariants; Integrability; singularities solutions; shock waves and phase transitions
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue of the journal will be devoted to the following topics of thermodynamics and its applications:

  • Thermodynamics of complex systems equipped with inner structures and inner symmetries. Methods of finding and study their state Lagrangian manifolds and state equations.
  • Critical phenomena and phase transitions for solutions of non-linear PDEs and especially critical phenomena in fluid motions.
  • Phase transitions, critical exponents, and their relations with theory of Lagrangian singularities.
  • Control theory of thermodynamical processes, and especially processes with phase transitions.

Prof. Dr. Lychagin Valentin
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.

Keywords

  • Phase transition
  • Lagrangian singularity
  • State equation
  • Critical exponent
  • Inner symmetry

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Published Papers (4 papers)

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Research

18 pages, 1103 KiB  
Article
On Energy–Information Balance in Automatic Control Systems Revisited
by Vladimir Rubtsov
Entropy 2020, 22(11), 1300; https://doi.org/10.3390/e22111300 - 15 Nov 2020
Viewed by 1473
Abstract
We revise and slightly generalize some variational problems related to the “informational approach” in the classical optimization problem for automatic control systems which was popular from 1970–1990. We find extremals for various degenerated (derivative independent) functionals and propose some interpretations of obtained minimax [...] Read more.
We revise and slightly generalize some variational problems related to the “informational approach” in the classical optimization problem for automatic control systems which was popular from 1970–1990. We find extremals for various degenerated (derivative independent) functionals and propose some interpretations of obtained minimax relations. The main example of such functionals is given by the Gelfand–Pinsker–Yaglom formula for the information quantity contained in one random process in another one. We find some balance relations in a linear stationary one-dimensional system with Gaussian signal and interpret them in terms of Legendre duality. Full article
(This article belongs to the Special Issue Thermodynamics, Geometry and Control Theory)
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8 pages, 878 KiB  
Article
On Higher Order Structures in Thermodynamics
by Valentin Lychagin and Mikhail Roop
Entropy 2020, 22(10), 1147; https://doi.org/10.3390/e22101147 - 12 Oct 2020
Cited by 2 | Viewed by 1960
Abstract
We present the development of the approach to thermodynamics based on measurement. First of all, we recall that considering classical thermodynamics as a theory of measurement of extensive variables one gets the description of thermodynamic states as Legendrian or Lagrangian manifolds representing the [...] Read more.
We present the development of the approach to thermodynamics based on measurement. First of all, we recall that considering classical thermodynamics as a theory of measurement of extensive variables one gets the description of thermodynamic states as Legendrian or Lagrangian manifolds representing the average of measurable quantities and extremal measures. Secondly, the variance of random vectors induces the Riemannian structures on the corresponding manifolds. Computing higher order central moments, one drives to the corresponding higher order structures, namely the cubic and the fourth order forms. The cubic form is responsible for the skewness of the extremal distribution. The condition for it to be zero gives us so-called symmetric processes. The positivity of the fourth order structure gives us an additional requirement to thermodynamic state. Full article
(This article belongs to the Special Issue Thermodynamics, Geometry and Control Theory)
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19 pages, 313 KiB  
Article
Differential Invariants of Measurements, and Their Relation to Central Moments
by Eivind Schneider
Entropy 2020, 22(10), 1118; https://doi.org/10.3390/e22101118 - 3 Oct 2020
Cited by 5 | Viewed by 1521
Abstract
Due to the principle of minimal information gain, the measurement of points in an affine space V determines a Legendrian submanifold of V×V*×R. Such Legendrian submanifolds are equipped with additional geometric structures that come from the central [...] Read more.
Due to the principle of minimal information gain, the measurement of points in an affine space V determines a Legendrian submanifold of V×V*×R. Such Legendrian submanifolds are equipped with additional geometric structures that come from the central moments of the underlying probability distributions and are invariant under the action of the group of affine transformations on V. We investigate the action of this group of affine transformations on Legendrian submanifolds of V×V*×R by giving a detailed overview of the structure of the algebra of scalar differential invariants, and we show how the scalar differential invariants can be constructed from the central moments. In the end, we view the results in the context of equilibrium thermodynamics of gases, and notice that the heat capacity is one of the differential invariants. Full article
(This article belongs to the Special Issue Thermodynamics, Geometry and Control Theory)
14 pages, 784 KiB  
Article
Optimal Thermodynamic Processes For Gases
by Alexei Kushner, Valentin Lychagin and Mikhail Roop
Entropy 2020, 22(4), 448; https://doi.org/10.3390/e22040448 - 15 Apr 2020
Cited by 14 | Viewed by 2780
Abstract
In this paper, we consider an optimal control problem in the equilibrium thermodynamics of gases. The thermodynamic state of the gas is given by a Legendrian submanifold in a contact thermodynamic space. Using Pontryagin’s maximum principle, we find a thermodynamic process in this [...] Read more.
In this paper, we consider an optimal control problem in the equilibrium thermodynamics of gases. The thermodynamic state of the gas is given by a Legendrian submanifold in a contact thermodynamic space. Using Pontryagin’s maximum principle, we find a thermodynamic process in this submanifold such that the gas maximizes the work functional. For ideal gases, this problem is shown to be integrable in Liouville’s sense and its solution is given by means of action-angle variables. For real gases considered to be a perturbation of ideal ones, the integrals are given asymptotically. Full article
(This article belongs to the Special Issue Thermodynamics, Geometry and Control Theory)
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