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Entropy
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Advances in Relativistic Statistical Mechanics II
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Advances in Relativistic Statistical Mechanics II

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

Deadline for manuscript submissions: closed (20 December 2022) | Viewed by 5508

Special Issue Editors

Prof. Dr. Asher Yahalom

E-Mail Website
Guest Editor
Department of Electrical and Electronic Engineering, Ariel University, Ariel 40700, Israel
Interests: relativistic dynamics and relativistic engines; non-barotropic (entropy dependent) fluid dynamics and magnetohydrodynamics; topological conservation laws in entropy dependent flow dynamics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Lawrence Horwitz

E-Mail Website1 Website2
Guest Editor
1. Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
2. Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel
3. Department of Physics, Ariel University, Ariel 40700, Israel
Interests: relativistic quantum mechanics and quantum field theory; theory of classical and quantum unstable systems and chaos; quantum theory on hypercomplex Hilbert modules; complex projective spaces in quantum dynamics; relativistic statistical mechanics and thermodynamics; high-energy nuclear structure and particle physics
Special Issues, Collections and Topics in MDPI journals
Dr. Prachi Sharma

E-Mail Website
Co-Guest Editor
Department of Electrical and Electronic Engineering, Ariel University, Ariel 40700, Israel
Interests: magnetohydrodynamics; turbulence; ponderomotive nonlinearity; solar corona

Special Issue Information

Dear Colleagues,

Relativistic statistical mechanics, with the work of Max Planck, lies at the very foundations of quantum theory. Major theoretical steps were made by Synge, de Groot, Israel and Kandrup, Haber and Weldon, Hakim, Horwitz, Schieve and Piron, among others; recent experiments and high-precision observations have motivated the growing interest in and importance of this subject.

Both the classical and quantum theories of relativistic many-body systems have been developed over the years, with important applications in many areas, such as plasma physics, also associated with the fusion problem, high-energy particle physics (as in the work of Oppenheimer and Hagedorn, and observations and interpretations of deep inelastic scattering), and high-frequency electronic devices, such as the free-electron laser, relativistic electron tubes, and dissipative relativistic hydrodynamics.

The significance of relativistic statistical mechanics is also of great importance in the framework of general relativity and cosmology, such as stellar structures, studies of instabilities as in supernova events, dark matter and dark energy problems, and black hole physics. There have, for example, been recent attempts to define entropic processes in connection with the geometric configuration of geodesic curves on the space–time manifold.

This Special Issue of Entropy will collect recent developments to motivate and stimulate further research in this important field.

Prof. Dr. Asher Yahalom
Prof. Dr. Lawrence Horwitz
Dr. Prachi Sharma
Guest Editors

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

  • Relativity
  • Fluid mechanics
  • Plasma physics
  • Many-body physics
  • High energy scattering
  • High energy electron tubes
  • High energy nuclear structure
  • Free-electron lasers
  • Stellar structure
  • Cosmology

Published Papers (3 papers)

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Research

12 pages, 329 KiB  
Article
Pauli’s Electron in Ehrenfest and Bohm Theories, a Comparative Study
by Asher Yahalom
Entropy 2023, 25(2), 190; https://doi.org/10.3390/e25020190 - 18 Jan 2023
Cited by 2 | Viewed by 1323
Abstract
Electrons moving at slow speeds much lower than the speed of light are described by a wave function which is a solution of Pauli’s equation. This is a low-velocity limit of the relativistic Dirac equation. Here we compare two approaches, one of which [...] Read more.
Electrons moving at slow speeds much lower than the speed of light are described by a wave function which is a solution of Pauli’s equation. This is a low-velocity limit of the relativistic Dirac equation. Here we compare two approaches, one of which is the more conservative Copenhagen’s interpretation denying a trajectory of the electron but allowing a trajectory to the electron expectation value through the Ehrenfest theorem. The said expectation value is of course calculated using a solution of Pauli’s equation. A less orthodox approach is championed by Bohm, and attributes a velocity field to the electron also derived from the Pauli wave function. It is thus interesting to compare the trajectory followed by the electron according to Bohm and its expectation value according to Ehrenfest. Both similarities and differences will be considered. Full article
(This article belongs to the Special Issue Advances in Relativistic Statistical Mechanics II)
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26 pages, 4245 KiB  
Article
Entanglement Dynamics of Coupled Quantum Oscillators in Independent NonMarkovian Baths
by Jen-Tsung Hsiang, Onat Arısoy and Bei-Lok Hu
Entropy 2022, 24(12), 1814; https://doi.org/10.3390/e24121814 - 13 Dec 2022
Cited by 7 | Viewed by 1807
Abstract
This work strives to better understand how the entanglement in an open quantum system, here represented by two coupled Brownian oscillators, is affected by a nonMarkovian environment (with memories), here represented by two independent baths each oscillator separately interacts with. We consider two [...] Read more.
This work strives to better understand how the entanglement in an open quantum system, here represented by two coupled Brownian oscillators, is affected by a nonMarkovian environment (with memories), here represented by two independent baths each oscillator separately interacts with. We consider two settings, a ‘symmetric’ configuration wherein the parameters of both oscillators and their baths are identical, and an ‘asymmetric’ configuration wherein they are different, in particular, a ‘hybrid’ configuration, where one of the two coupled oscillators interacts with a nonMarkovian bath and the other with a Markovian bath. Upon finding the solutions to the Langevin equations governing the system dynamics and the evolution of the covariance matrix elements entering into its entanglement dynamics, we ask two groups of questions: (Q1) Which time regime does the bath’s nonMarkovianity benefit the system’s entanglement most? The answers we get from detailed numerical studies suggest that (A1) For an initially entangled pair of oscillators, we see that in the intermediate time range, the duration of entanglement is proportional to the memory time, and it lasts a fraction of the relaxation time, but at late times when the dynamics reaches a steady state, the value of the symplectic eigenvalue of the partially transposed covariance matrix barely benefit from the bath nonMarkovianity. For the second group of questions: (Q2) Can the memory of one nonMarkovian bath be passed on to another Markovian bath? And if so, does this memory transfer help to sustain the system’s entanglement dynamics? Our results from numerical studies of the asymmetric hybrid configuration indicate that (A2) A system with a short memory time can acquire improvement when it is coupled to another system with a long memory time, but, at a cost of the latter. The sustainability of the bipartite entanglement is determined by the party which breaks off entanglement most easily. Full article
(This article belongs to the Special Issue Advances in Relativistic Statistical Mechanics II)
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8 pages, 564 KiB  
Article
First-Principle Derivation of Single-Photon Entropy and Maxwell–Jüttner Velocity Distribution
by Changhao Li, Jianfeng Li and Yuliang Yang
Entropy 2022, 24(11), 1609; https://doi.org/10.3390/e24111609 - 4 Nov 2022
Cited by 2 | Viewed by 1591
Abstract
This work is devoted to deriving the entropy of a single photon in a beam of light from first principles. Based on the quantum processes of light–matter interaction, we find that, if the light is not in equilibrium, there are two different ways, [...] Read more.
This work is devoted to deriving the entropy of a single photon in a beam of light from first principles. Based on the quantum processes of light–matter interaction, we find that, if the light is not in equilibrium, there are two different ways, depending on whether the photon is being added or being removed from the light, of defining the single-photon entropy of this light. However, when the light is in equilibrium at temperature T, the two definitions are equivalent and the photon entropy of this light is hν/T. From first principles, we also re-derive the Jüttner velocity distribution showing that, even without interatomic collisions, two-level atoms will relax to the state satisfying the Maxwell–Jüttner velocity distribution when they are moving in blackbody radiation fields. Full article
(This article belongs to the Special Issue Advances in Relativistic Statistical Mechanics II)
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