Special Issue "Time and Entropy"

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

Deadline for manuscript submissions: closed (30 October 2020).

Special Issue Editor

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
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Special Issue Information

Dear Colleagues,

The relation between time and entropy goes back as far as the formulation of the second law of thermodynamics, i.e., that in any isolated system the entropy increases monotonically in time, thereby establishing a relation between entropy and the direction of time.

In recent years, major developments have taken place. Analytic methods have been developed for studying the direction of time in the evolution of quantum states, and the study of resonances and their decay by Lax and Phillips in 1967 have opened new directions of investigation in electromagnetic radiation and the quantum theory for the study of irreversible, entropic, processes.

In the framework of more recently developed approaches to relativistic statistical mechanics, the corresponding Boltzmann equation maintains a monotonic relation between the Einstein time t (as occurs, for example, in the Maxwell equations) and the growth of entropy for particles. For the evolution of antiparticles, which move backward in time (before charge conjugation), the entropy appears to decrease in the relativistically defined time. However, the monotonic increase in entropy is maintained in invariant world time. There has been, moreover, recent discussion of the embedding of this special relativistic theory into the framework of general relativity, opening the possibility of describing the notions of relativistic statistical mechanics and its corresponding entropic properties, on a cosmic scale, to stellar phenomena, astrophysics and cosmology.
We anticipate contributions to this special issue which will deal with these newly developing topics.

Prof. Lawrence P. Horwitz
Guest Editor

Manuscript Submission Information

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Keywords

  • direction of time
  • unstable systems
  • resonances
  • time as an observable
  • Boltzmann equation
  • relativistic evolution
  • antiparticles
  • astrophysics
  • cosmology

Published Papers (5 papers)

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Research

Open AccessArticle
Entropy and the Direction of Time
Entropy 2021, 23(4), 388; https://doi.org/10.3390/e23040388 - 25 Mar 2021
Viewed by 383
Abstract
The paper tries to demonstrate that the process of the increase of entropy does not explain the asymmetry of time itself because it is unable to account for its fundamental asymmetries, that is, the asymmetry of traces (we have traces of the past [...] Read more.
The paper tries to demonstrate that the process of the increase of entropy does not explain the asymmetry of time itself because it is unable to account for its fundamental asymmetries, that is, the asymmetry of traces (we have traces of the past and no traces of the future), the asymmetry of causation (we have an impact on future events with no possibility of having an impact on the past), and the asymmetry between the fixed past and the open future, To this end, the approaches of Boltzmann, Reichenbach (and his followers), and Albert are analysed. It is argued that we should look for alternative approaches instead of this, namely we should consider a temporally asymmetrical physical theory or seek a source of the asymmetry of time in metaphysics. This second approach may even turn out to be complementary if only we accept that metaphysics can complement scientific research programmes. Full article
(This article belongs to the Special Issue Time and Entropy)
Open AccessArticle
Efficient Markets and Contingent Claims Valuation: An Information Theoretic Approach
Entropy 2020, 22(11), 1283; https://doi.org/10.3390/e22111283 - 12 Nov 2020
Viewed by 1113
Abstract
This research article shows how the pricing of derivative securities can be seen from the context of stochastic optimal control theory and information theory. The financial market is seen as an information processing system, which optimizes an information functional. An optimization problem is [...] Read more.
This research article shows how the pricing of derivative securities can be seen from the context of stochastic optimal control theory and information theory. The financial market is seen as an information processing system, which optimizes an information functional. An optimization problem is constructed, for which the linearized Hamilton–Jacobi–Bellman equation is the Black–Scholes pricing equation for financial derivatives. The model suggests that one can define a reasonable Hamiltonian for the financial market, which results in an optimal transport equation for the market drift. It is shown that in such a framework, which supports Black–Scholes pricing, the market drift obeys a backwards Burgers equation and that the market reaches a thermodynamical equilibrium, which minimizes the free energy and maximizes entropy. Full article
(This article belongs to the Special Issue Time and Entropy)
Open AccessArticle
The Relativistic Boltzmann Equation and Two Times
Entropy 2020, 22(8), 804; https://doi.org/10.3390/e22080804 - 22 Jul 2020
Viewed by 699
Abstract
We discuss a covariant relativistic Boltzmann equation which describes the evolution of a system of particles in spacetime evolving with a universal invariant parameter τ . The observed time t of Einstein and Maxwell, in the presence of interaction, is not necessarily a monotonic function of τ . If t ( τ ) increases with τ , the worldline may be associated with a normal particle, but if it is decreasing in τ , it is observed in the laboratory as an antiparticle. This paper discusses the implications for entropy evolution in this relativistic framework. It is shown that if an ensemble of particles and antiparticles, converge in a region of pair annihilation, the entropy of the antiparticle beam may decreaase in time. Full article
(This article belongs to the Special Issue Time and Entropy)
Open AccessArticle
Entropy and Time
Entropy 2020, 22(4), 430; https://doi.org/10.3390/e22040430 - 10 Apr 2020
Cited by 2 | Viewed by 1077
Abstract
The idea that entropy is associated with the “arrow of time” has its roots in Clausius’s statement on the Second Law: “Entropy of the Universe always increases.” However, the explicit association of the entropy with time’s arrow arises from Eddington. In [...] Read more.
The idea that entropy is associated with the “arrow of time” has its roots in Clausius’s statement on the Second Law: “Entropy of the Universe always increases.” However, the explicit association of the entropy with time’s arrow arises from Eddington. In this article, we start with a brief review of the idea that the “increase in entropy” is somehow associated with the direction in which time increases. Then, we examine three different, but equivalent definitions of entropy. We find that none of these definitions indicate any hint of a relationship between entropy and time. We can, therefore, conclude that entropy is a timeless quantity. We also discuss the reasons as to why some scientists went astray in associating entropy with time’s arrow. Finally, we shall discuss Boltzmann’s H-Theorem, which is viewed by many as a proof of the Second Law of Thermodynamics. Full article
(This article belongs to the Special Issue Time and Entropy)
Open AccessEditor’s ChoiceArticle
Maxwell’s Demon in Quantum Mechanics
Entropy 2020, 22(3), 269; https://doi.org/10.3390/e22030269 - 27 Feb 2020
Cited by 1 | Viewed by 1377
Abstract
Maxwell’s Demon is a thought experiment devised by J. C. Maxwell in 1867 in order to show that the Second Law of thermodynamics is not universal, since it has a counter-example. Since the Second Law is taken by many to provide an arrow [...] Read more.
Maxwell’s Demon is a thought experiment devised by J. C. Maxwell in 1867 in order to show that the Second Law of thermodynamics is not universal, since it has a counter-example. Since the Second Law is taken by many to provide an arrow of time, the threat to its universality threatens the account of temporal directionality as well. Various attempts to “exorcise” the Demon, by proving that it is impossible for one reason or another, have been made throughout the years, but none of them were successful. We have shown (in a number of publications) by a general state-space argument that Maxwell’s Demon is compatible with classical mechanics, and that the most recent solutions, based on Landauer’s thesis, are not general. In this paper we demonstrate that Maxwell’s Demon is also compatible with quantum mechanics. We do so by analyzing a particular (but highly idealized) experimental setup and proving that it violates the Second Law. Our discussion is in the framework of standard quantum mechanics; we give two separate arguments in the framework of quantum mechanics with and without the projection postulate. We address in our analysis the connection between measurement and erasure interactions and we show how these notions are applicable in the microscopic quantum mechanical structure. We discuss what might be the quantum mechanical counterpart of the classical notion of “macrostates”, thus explaining why our Quantum Demon setup works not only at the micro level but also at the macro level, properly understood. One implication of our analysis is that the Second Law cannot provide a universal lawlike basis for an account of the arrow of time; this account has to be sought elsewhere. Full article
(This article belongs to the Special Issue Time and Entropy)
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