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Matter-Aggregating Systems at a Classical vs. Quantum Interface

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

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 4892

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Special Issue Editors

Prof. Dr. Adam Gadomski

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Institute of Mathematics and Physics, Faculty of Chemical Technology and Engineering, Bydgoszcz University of Science and Technology, Al. Kaliskiego 7, 85-796 Bydgoszcz, Poland
Interests: statistical mechanics; soft condensed matter; (bio)materials nanophysics
Special Issues, Collections and Topics in MDPI journals

Dr. Natalia Kruszewska

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Institute of Mathematics and Physics, Faculty of Chemical Technology and Engineering, Bydgoszcz University of Science and Technology, Al. Kaliskiego 7, 85-796 Bydgoszcz, Poland
Interests: theoretical physics; statistical and computational physics; soft matter physics; biophysics; complex networks

Special Issue Information

Dear Colleagues,

Matter-aggregating systems, such as spin-involving (Ising, Potts, etc.), dipolar, percolating, or those prone to gelation and/or colloidal formations and self-assembly, to mention but a few, can be viewed as prerequisites of paradigmatic cluster/network formations, ranging from classical to quantum expositions.

There is no general statistical–physical or (soft) condensed matter theoretical description of matter aggregation as it is. However, a robust theoretical framework exists based on the nucleation–growth phase transition concept, entirely related to continuous (or second-order) phase transitions and/or order–disorder and polymorphic phase change concepts. The overall framework is based on the renormalization group approach, and it often employs the scaling concept as a foundation for cooperation with computer-simulation-related solutions to matter aggregation problems, considered near thermodynamic (fairly close to entropy maximum) equilibrium.

Another extremely relevant issue related to aggregation appears to be a reduction in the system’s physical–geometrical dimensionality (toward the nanoscale) and/or any natural involvement of the fractal dimension concept, also in terms of unveiling certain matter evolutions using kinetic/dynamic equations, having included the suitable fractional operators, on the one hand. On the other hand, stochastic descriptions of the Fokker–Planck and Smoluchowski kinetically envisaged aggregations are equally appropriate, especially at the mesoscale. At this point, the conception of mesoscopic nonequilibrium (entropy-production-based) thermodynamics should also be indicated. In addition, solving the problems using machine learning, and artificial intelligence techniques in general, would be an asset.

The challenge of the proposed Special Issue lies in thoroughly exploring the matter-aggregational outcomes of any type for which a classical–quantum interface is going to readily emerge as it is—for example, in the case of low-dimensional (nano)structures or complex classical–quantum (also biopolymeric) networks in which entanglement and bond creation effects prevail.

The collected articles have to unambiguously show that the linkage between the classical and quantum formations is worth exploring and may become very practical from the point of view of modern quantum (nano)technologies, with an emphasis placed on the nanoscale as the sovereign physical border between classical and quantum realms. The Special Issue is mainly addressed to statistical and soft condensed-matter physicists, chemical physics and physical chemistry (computational) specialists, as well as (bio)materials scientists and advanced technology engineers.

Prof. Dr. Adam Gadomski
Dr. Natalia Kruszewska
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

matter aggregation
classical vs. quantum
stochastic quantization
nanostructure formation
Fokker–Planck and Smoluchowski equations
(dis)ordered cluster–cluster aggregation
diffusion vs. Schroedinger approach
phase transitions
mesostructures
entropy production
complex networks
stochasticity
entanglement
interfacial phenomena
reduction in physical dimensionality

Published Papers (4 papers)

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Research

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26 pages, 1605 KiB

Open AccessFeature PaperArticle

Canonical vs. Grand Canonical Ensemble for Bosonic Gases under Harmonic Confinement

by Andrea Crisanti, Luca Salasnich, Alessandro Sarracino and Marco Zannetti

Entropy 2024, 26(5), 367; https://doi.org/10.3390/e26050367 - 26 Apr 2024

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Abstract

We analyze the general relation between canonical and grand canonical ensembles in the thermodynamic limit. We begin our discussion by deriving, with an alternative approach, some standard results first obtained by Kac and coworkers in the late 1970s. Then, motivated by the Bose–Einstein condensation (BEC) of trapped gases with a fixed number of atoms, which is well described by the canonical ensemble and by the recent groundbreaking experimental realization of BEC with photons in a dye-filled optical microcavity under genuine grand canonical conditions, we apply our formalism to a system of non-interacting Bose particles confined in a two-dimensional harmonic trap. We discuss in detail the mathematical origin of the inequivalence of ensembles observed in the condensed phase, giving place to the so-called grand canonical catastrophe of density fluctuations. We also provide explicit analytical expressions for the internal energy and specific heat and compare them with available experimental data. For these quantities, we show the equivalence of ensembles in the thermodynamic limit. Full article

(This article belongs to the Special Issue Matter-Aggregating Systems at a Classical vs. Quantum Interface)

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14 pages, 5184 KiB

Open AccessArticle

(Non)Resonance Bonds in Molecular Dynamics Simulations: A Case Study concerning C₆₀ Fullerenes

by Jacek Siódmiak

Entropy 2024, 26(3), 214; https://doi.org/10.3390/e26030214 - 28 Feb 2024

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Abstract

In the case of certain chemical compounds, especially organic ones, electrons can be delocalized between different atoms within the molecule. These resulting bonds, known as resonance bonds, pose a challenge not only in theoretical descriptions of the studied system but also present difficulties in simulating such systems using molecular dynamics methods. In computer simulations of such systems, it is often common practice to use fractional bonds as an averaged value across equivalent structures, known as a resonance hybrid. This paper presents the results of the analysis of five forms of C₆₀ fullerene polymorphs: one with all bonds being resonance, three with all bonds being integer (singles and doubles in different configurations), one with the majority of bonds being integer (singles and doubles), and ten bonds (within two opposite pentagons) valued at one and a half. The analysis involved the Shannon entropy value for bond length distributions and the eigenfrequency of intrinsic vibrations (first vibrational mode), reflecting the stiffness of the entire structure. The maps of the electrostatic potential distribution around the investigated structures are presented and the dipole moment was estimated. Introducing asymmetry in bond redistribution by incorporating mixed bonds (integer and partial), in contrast to variants with equivalent bonds, resulted in a significant change in the examined observables. Full article

(This article belongs to the Special Issue Matter-Aggregating Systems at a Classical vs. Quantum Interface)

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11 pages, 991 KiB

Open AccessArticle

(Nano)Granules-Involving Aggregation at a Passage to the Nanoscale as Viewed in Terms of a Diffusive Heisenberg Relation

by Adam Gadomski

Entropy 2024, 26(1), 76; https://doi.org/10.3390/e26010076 - 17 Jan 2024

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Abstract

We are looking at an aggregation of matter into granules. Diffusion plays a pivotal role here. When going down to the nanometer scale (the so-called nanoscale quantum-size effect limit), quantum mechanics, and the Heisenberg uncertainty relation, may take over the role of classical diffusion, as viewed typically in the mesoscopic/stochastic limit. A d-dimensional entropy-production aggregation of the granules-involving matter in the granule-size space is considered in terms of a (sub)diffusive realization. It turns out that when taking a full d-dimensional pathway of the aggregation toward the nanoscale, one is capable of disclosing a Heisenberg-type (diffusional) relation, setting up an upper uncertainty bound for the (sub)diffusive, very slow granules-including environment that, within the granule-size analogy invoked, matches the quantum limit of h/2πμ (μ—average mass of a granule; h—the Planck’s constant) for the diffusion coefficient of the aggregation, first proposed by Fürth in 1933 and qualitatively foreseen by Schrödinger some years before, with both in the context of a diffusing particle. The classical quantum passage uncovered here, also termed insightfully as the quantum-size effect (as borrowed from the quantum dots’ parlance), works properly for the three-dimensional (d = 3) case, making use of a substantial physical fact that the (nano)granules interact readily via their surfaces with the also-granular surroundings in which they are immersed. This natural observation is embodied in the basic averaging construction of the diffusion coefficient of the entropy-productive (nano)aggregation of interest. Full article

(This article belongs to the Special Issue Matter-Aggregating Systems at a Classical vs. Quantum Interface)

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Review

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14 pages, 1657 KiB

Open AccessReview

Thermodynamic Insights into Symmetry Breaking: Exploring Energy Dissipation across Diverse Scales

by Andrés Arango-Restrepo and J. Miguel Rubi

Entropy 2024, 26(3), 231; https://doi.org/10.3390/e26030231 - 5 Mar 2024

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Abstract

Symmetry breaking is a phenomenon that is observed in various contexts, from the early universe to complex organisms, and it is considered a key puzzle in understanding the emergence of life. The importance of this phenomenon is underscored by the prevalence of enantiomeric amino acids and proteins.The presence of enantiomeric amino acids and proteins highlights its critical role. However, the origin of symmetry breaking has yet to be comprehensively explained, particularly from an energetic standpoint. This article explores a novel approach by considering energy dissipation, specifically lost free energy, as a crucial factor in elucidating symmetry breaking. By conducting a comprehensive thermodynamic analysis applicable across scales, ranging from elementary particles to aggregated structures such as crystals, we present experimental evidence establishing a direct link between nonequilibrium free energy and energy dissipation during the formation of the structures. Results emphasize the pivotal role of energy dissipation, not only as an outcome but as the trigger for symmetry breaking. This insight suggests that understanding the origins of complex systems, from cells to living beings and the universe itself, requires a lens focused on nonequilibrium processes Full article

(This article belongs to the Special Issue Matter-Aggregating Systems at a Classical vs. Quantum Interface)

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