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Entropy
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Quantum Mechanics and the Challenge of Time
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Quantum Mechanics and the Challenge of Time

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

Deadline for manuscript submissions: 15 October 2025 | Viewed by 4921

Special Issue Editors

Prof. Eli Pollak

E-Mail Website
Guest Editor
Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel
Interests: theoretical chemistry; physics and molecular dynamics
Prof. Randall S. Dumont

E-Mail Website
Guest Editor
Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON L8S 4M1, Canada
Interests: relativistic quantum dynamics; quantum and semiclassical molecular dynamics; simulation of NMR spectra

Special Issue Information

Dear Colleagues,

Much progress has been made in the past ten years, both theoretically as well as experimentally, in our understanding of the role of time in quantum mechanics. Yet many questions remain unanswered, such as what is the duration of a quantum transition? Will quantum mechanics speed up or slow down dynamical processes? How does spin symmetry affect transition times? The enigma of energy–time–uncertainty relations has not been fully resolved. Is there a measurable time operator? What is the relation between the time and spatial axes, especially when considering quantum mechanics in the relativistic limit? The purpose of this Special Issue is to provide the reader with new results and a feeling for the role of time in quantum mechanics, a topic which continues to intrigue us all.

Prof. Eli Pollak
Prof. Randall S. Dumont
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.

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Published Papers (4 papers)

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Research

30 pages, 524 KiB  
Article
Two Types of Temporal Symmetry in the Laws of Nature
by A. Y. Klimenko
Entropy 2025, 27(5), 466; https://doi.org/10.3390/e27050466 - 25 Apr 2025
Viewed by 138
Abstract
This work explores the implications of assuming time symmetry and applying bridge-type, time-symmetric temporal boundary conditions to deterministic laws of nature with random components. The analysis, drawing on the works of Kolmogorov and Anderson, leads to two forms of governing equations, referred to [...] Read more.
This work explores the implications of assuming time symmetry and applying bridge-type, time-symmetric temporal boundary conditions to deterministic laws of nature with random components. The analysis, drawing on the works of Kolmogorov and Anderson, leads to two forms of governing equations, referred to here as symmetric and antisymmetric. These equations account for the emergence of characteristics associated with conventional thermodynamics, the arrow of time, and a form of antecedent causality. The directional properties of time arise from the mathematical structure of Markov bridges in proximity of the corresponding temporal boundary conditions, without requiring any postulates that impose a preferred direction of time. Full article
(This article belongs to the Special Issue Quantum Mechanics and the Challenge of Time)
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23 pages, 5859 KiB  
Article
On Dynamical Measures of Quantum Information
by James Fullwood and Arthur J. Parzygnat
Entropy 2025, 27(4), 331; https://doi.org/10.3390/e27040331 - 21 Mar 2025
Viewed by 238
Abstract
In this work, we use the theory of quantum states over time to define joint entropy for timelike-separated quantum systems. For timelike-separated systems that admit a dual description as being spacelike-separated, our notion of entropy recovers the usual von Neumann entropy for bipartite [...] Read more.
In this work, we use the theory of quantum states over time to define joint entropy for timelike-separated quantum systems. For timelike-separated systems that admit a dual description as being spacelike-separated, our notion of entropy recovers the usual von Neumann entropy for bipartite quantum states and thus may be viewed as a spacetime generalization of von Neumann entropy. Such an entropy is then used to define dynamical extensions of quantum joint entropy, quantum conditional entropy, and quantum mutual information for systems separated by the action of a quantum channel. We provide an in-depth mathematical analysis of such information measures and the properties they satisfy. We also use such a dynamical formulation of entropy to quantify the information loss/gain associated with the dynamical evolution of quantum systems, which enables us to formulate a precise notion of information conservation for quantum processes. Finally, we show how our dynamical entropy admits an operational interpretation in terms of quantifying the amount of state disturbance associated with a positive operator- valued measurement. Full article
(This article belongs to the Special Issue Quantum Mechanics and the Challenge of Time)
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28 pages, 604 KiB  
Article
Dwell Times, Wavepacket Dynamics, and Quantum Trajectories for Particles with Spin 1/2
by Bill Poirier and Richard Lombardini
Entropy 2024, 26(4), 336; https://doi.org/10.3390/e26040336 - 14 Apr 2024
Viewed by 2185
Abstract
The theoretical connections between quantum trajectories and quantum dwell times, previously explored in the context of 1D time-independent stationary scattering applications, are here generalized for multidimensional time-dependent wavepacket applications for particles with spin 1/2. In addition to dwell times, trajectory-based dwell time distributions [...] Read more.
The theoretical connections between quantum trajectories and quantum dwell times, previously explored in the context of 1D time-independent stationary scattering applications, are here generalized for multidimensional time-dependent wavepacket applications for particles with spin 1/2. In addition to dwell times, trajectory-based dwell time distributions are also developed, and compared with previous distributions based on the dwell time operator and the flux–flux correlation function. Dwell time distributions are of interest, in part because they may be of experimental relevance. In addition to standard unipolar quantum trajectories, bipolar quantum trajectories are also considered, and found to relate more directly to the dwell time (and other quantum time) quantities of greatest relevance for scattering applications. Detailed calculations are performed for a benchmark 3D spin-1/2 particle application, considered previously in the context of computing quantum arrival times. Full article
(This article belongs to the Special Issue Quantum Mechanics and the Challenge of Time)
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17 pages, 1843 KiB  
Article
Quantum Measurements and Delays in Scattering by Zero-Range Potentials
by Xabier Gutiérrez, Marisa Pons and Dmitri Sokolovski
Entropy 2024, 26(1), 75; https://doi.org/10.3390/e26010075 - 16 Jan 2024
Cited by 1 | Viewed by 1569
Abstract
Eisenbud–Wigner–Smith delay and the Larmor time give different estimates for the duration of a quantum scattering event. The difference is most pronounced in the case where the de Broglie wavelength is large compared to the size of the scatterer. We use the methods [...] Read more.
Eisenbud–Wigner–Smith delay and the Larmor time give different estimates for the duration of a quantum scattering event. The difference is most pronounced in the case where the de Broglie wavelength is large compared to the size of the scatterer. We use the methods of quantum measurement theory to analyse both approaches and to decide which one of them, if any, describes the duration a particle spends in the region that contains the scattering potential. The cases of transmission, reflection, and three-dimensional elastic scattering are discussed in some detail. Full article
(This article belongs to the Special Issue Quantum Mechanics and the Challenge of Time)
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