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The Ubiquity of Entropy II

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

Deadline for manuscript submissions: closed (30 April 2022) | Viewed by 9080

Special Issue Editor

QSTAR and Istituto Nazionale di Ottica CNR, Largo Enrico Fermi 2, Florence, Italy
Interests: statistical mechanics; phase-transitions; microcanonical ensemble; entropy; Fisher information
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Entropy is one of the most important concepts in physics. Its prominent role in the description of macroscopic systems was first recognized by Clausius, Maxwell, Kelvin, Boltzmann, and many others when the foundations of Statistical Mechanics were laid. Since then, the domain of application of the concept of entropy has been greatly extended, and entropy is now regarded as a paradigm with which the most intriguing challenges of modern physics are faced.

Among these, we find the description of finite classical and quantum systems, at the nanoscopic scale, that are now considered an essential part of forthcoming (bio-)technologies. To name just a few emblematic problems whose solutions still remain elusive, we mention the quantitative characterization of the complexity of classical and quantum systems and the qualification and quantification of entanglement in quantum systems.

In the present Issue, pioneering works are considered in which the concept of entropy is applied in order to provided advances, for instance, in the description of the following:

  1. Complex networks that describe biological, social, economic, or dynamical systems;
  2. Complex quantum models that are used for the characterization of complexity quantum networks, in the quantum machine-learning problem, or in the development of quantum technologies.

Dr. Roberto Franzosi
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

  • finite systems
  • complex systems
  • quantum complex systems
  • entanglement
  • statistical mechanics

Published Papers (3 papers)

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Research

6 pages, 255 KiB  
Article
Memory and Entropy
by Carlo Rovelli
Entropy 2022, 24(8), 1022; https://doi.org/10.3390/e24081022 - 24 Jul 2022
Cited by 3 | Viewed by 3774
Abstract
I study the physical nature of traces. Surprisingly, (i) systems separation with (ii) temperature differences and (iii) long thermalization times are sufficient conditions to produce macroscopic traces. Traces of the past are ubiquitous because these conditions are largely satisfied in our universe. I [...] Read more.
I study the physical nature of traces. Surprisingly, (i) systems separation with (ii) temperature differences and (iii) long thermalization times are sufficient conditions to produce macroscopic traces. Traces of the past are ubiquitous because these conditions are largely satisfied in our universe. I quantify these thermodynamical conditions for memory and derive an expression for the maximum amount of information stored in such memories as a function of the relevant thermodynamical parameters. This mechanism transforms low entropy into available information. I suggest that all macroscopic information has this origin in past low entropy. Full article
(This article belongs to the Special Issue The Ubiquity of Entropy II)
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17 pages, 1212 KiB  
Article
Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions
by Loris Di Cairano, Matteo Gori and Marco Pettini
Entropy 2021, 23(11), 1414; https://doi.org/10.3390/e23111414 - 27 Oct 2021
Cited by 3 | Viewed by 1866
Abstract
Different arguments led to supposing that the deep origin of phase transitions has to be identified with suitable topological changes of potential related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems [...] Read more.
Different arguments led to supposing that the deep origin of phase transitions has to be identified with suitable topological changes of potential related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of energy level submanifolds of the phase space. However, the sufficiency conditions are still a wide open question. In this study, a first important step forward was performed in this direction; in fact, a differential equation was worked out which describes how entropy varies as a function of total energy, and this variation is driven by the total energy dependence of a topology-related quantity of the relevant submanifolds of the phase space. Hence, general conditions can be in principle defined for topology-driven loss of differentiability of the entropy. Full article
(This article belongs to the Special Issue The Ubiquity of Entropy II)
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20 pages, 3620 KiB  
Article
Ground-State Properties and Phase Separation of Binary Mixtures in Mesoscopic Ring Lattices
by Vittorio Penna, Alessandra Contestabile and Andrea Richaud
Entropy 2021, 23(7), 821; https://doi.org/10.3390/e23070821 - 28 Jun 2021
Viewed by 2438
Abstract
We investigated the spatial phase separation of the two components forming a bosonic mixture distributed in a four-well lattice with a ring geometry. We studied the ground state of this system, described by means of a binary Bose–Hubbard Hamiltonian, by implementing a well-known [...] Read more.
We investigated the spatial phase separation of the two components forming a bosonic mixture distributed in a four-well lattice with a ring geometry. We studied the ground state of this system, described by means of a binary Bose–Hubbard Hamiltonian, by implementing a well-known coherent-state picture which allowed us to find the semi-classical equations determining the distribution of boson components in the ring lattice. Their fully analytic solutions, in the limit of large boson numbers, provide the boson populations at each well as a function of the interspecies interaction and of other significant model parameters, while allowing to reconstruct the non-trivial architecture of the ground-state four-well phase diagram. The comparison with the L-well (L=2,3) phase diagrams highlights how increasing the number of wells considerably modifies the phase diagram structure and the transition mechanism from the full-mixing to the full-demixing phase controlled by the interspecies interaction. Despite the fact that the phase diagrams for L=2,3,4 share various general properties, we show that, unlike attractive binary mixtures, repulsive mixtures do not feature a transition mechanism which can be extended to an arbitrary lattice of size L. Full article
(This article belongs to the Special Issue The Ubiquity of Entropy II)
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