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Condensed-Matter-Principia Based Information & Statistical Measures: From Classical to Quantum

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A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (20 December 2019) | Viewed by 38326

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Special Issue Editors

Prof. Dr. Adam Gadomski

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

Prof. Sylwia Zielińska-Raczyńska

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Institute of Mathematics and Physics, UTP University of Science and Technology, 85-796 Bydgoszcz, Poland
Interests: quantum optics; quantum information; photonics

Special Issue Information

Dear Colleagues,

Information, a relevant concern of this Special Issue, can be qualitatively defined as a noise-affected portion of an expected physical quantity transmitted from a sender to its receiving counterpart through a sender–receiver interface, also named an intermedium.

There is a substantiated knowledge accumulated about the routes of information transmission called, mostly, information channels. The intermedium can then be viewed as an ensemble of the channels: They can either be noisy or fairly noiseless.

The tercet, comprising the sender–receiver couple, and the intermedium, can be presented both classically and quantum-mechanically. A classic example is crystal growth from solution/melt, viewed as a sender, whereas the crystal surface zone mimics the receiver, and the entire crystal’s interface can be identified with the intermedium.

A quantum-mechanical example can be presented in terms of electrons transported along (carbon) nanotubes of different length and tortuosity, incorporated in a (bio)material’s sample, if operating out of Landauer’s ballistic-transport principia, thus experiencing tunneling conductivity conditions. Transport of quantum particles such as excitons is another valuable example.

The proposed Special Issue calls for papers dealing with physicochemical, condensed-matter systems, or their interdisciplinary analogs, for which really precise and well-defined classical vs. quantum information measures can be inferred, based preferably on the entropy concept.

It is envisaged that certain criteria such as those based on maximum entropy principle or entropy production for open thermodynamical systems will be applied using methods of statistical mechanics and quantum physics. Nonlinear (optoelectronic) complex systems’ peculiarities, different noise sources, and similar perturbative factors, such as distribution of defects and/or barriers to transport, as well as sources of chemical reactions spoiling a system’s directional behavior, are welcome to their incorporation in the Special Issue.

This Special Issue is devoted in part to recognizing the outstanding contribution to statistical thermodynamics and condensed matter physics by Professor Gerard Czajkowski, former institute director and vice rector for research at the UTP University of Science and Technology, Bydgoszcz, Poland.

The recognition is planned as Colloquium at UTP University of Science & Technology (Bydgoszcz, Poland), sponsored by the Marshal of Kujawsko-Pomorskie Voivodship in Toruń, Poland.

Prof. Adam Gadomski
Prof. Sylwia Zielińska-Raczyńska
Guest Editors

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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.

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Published Papers (11 papers)

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Editorial

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4 pages, 169 KiB

Open AccessEditorial

Information and Statistical Measures in Classical vs. Quantum Condensed-Matter and Related Systems

by Adam Gadomski and Sylwia Zielińska-Raczyńska

Entropy 2020, 22(6), 645; https://doi.org/10.3390/e22060645 - 10 Jun 2020

Cited by 2 | Viewed by 2014

Abstract

The presented editorial summarizes in brief the efforts of ten (10) papers collected by the Special Issue (SI) “Condensed-Matter-Principia Based Information & Statistical Measures: From Classical to Quantum”. The SI called for papers dealing with condensed-matter systems, or their interdisciplinary analogs, for which well-defined classical statistical vs. quantum information measures can be inferred while based on the entropy concept. The SI has mainly been rested upon objectives addressed by an international colloquium held in October 2019, at the University of Science and Technology (UTP) Bydgoszcz, Poland (see http://zmpf.imif.utp.edu.pl/rci-jcs/rci-jcs-4/), with an emphasis placed on the achievements of Professor Gerard Czajkowski (PGC). PGC commenced his research activity with diffusion-reaction (open) systems under the supervision of Roman S. Ingarden (Toruń), a father of Polish synergetics, and original thermodynamic approaches to self-organization. The active cooperation of PGC mainly with German physicists (Friedrich Schloegl, Aachen; Werner Ebeling, Berlin) ought to be underlined. Then, the development of Czajkowski’s research is worth underscoring, moving from statistical thermodynamics to solid state theory, pursued in terms of nonlinear solid-state optics (Franco Bassani, Pisa), and culminating very recently with large quasiparticles, termed Rydberg excitons, and their coherent interactions with light. Full article

(This article belongs to the Special Issue Condensed-Matter-Principia Based Information & Statistical Measures: From Classical to Quantum)

Research

Jump to: Editorial

12 pages, 1126 KiB

Open AccessArticle

Cross-Entropy as a Metric for the Robustness of Drone Swarms

by Piotr Cofta, Damian Ledziński, Sandra Śmigiel and Marta Gackowska

Entropy 2020, 22(6), 597; https://doi.org/10.3390/e22060597 - 27 May 2020

Cited by 10 | Viewed by 3026

Abstract

Due to their growing number and increasing autonomy, drones and drone swarms are equipped with sophisticated algorithms that help them achieve mission objectives. Such algorithms vary in their quality such that their comparison requires a metric that would allow for their correct assessment. The novelty of this paper lies in analysing, defining and applying the construct of cross-entropy, known from thermodynamics and information theory, to swarms. It can be used as a synthetic measure of the robustness of algorithms that can control swarms in the case of obstacles and unforeseen problems. Based on this, robustness may be an important aspect of the overall quality. This paper presents the necessary formalisation and applies it to a few examples, based on generalised unexpected behaviour and the results of collision avoidance algorithms used to react to obstacles. Full article

(This article belongs to the Special Issue Condensed-Matter-Principia Based Information & Statistical Measures: From Classical to Quantum)

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17 pages, 311 KiB

Open AccessArticle

Statistical Characteristics of Stationary Flow of Substance in a Network Channel Containing Arbitrary Number of Arms

by Roumen Borisov, Zlatinka I. Dimitrova and Nikolay K. Vitanov

Entropy 2020, 22(5), 553; https://doi.org/10.3390/e22050553 - 15 May 2020

Cited by 22 | Viewed by 3922

Abstract

We study flow of substance in a channel of network which consists of nodes of network and edges which connect these nodes and form ways for motion of substance. The channel can have arbitrary number of arms and each arm can contain arbitrary number of nodes. The flow of substance is modeled by a system of ordinary differential equations. We discuss first a model for a channel which arms contain infinite number of nodes each. For stationary regime of motion of substance in such a channel we obtain probability distributions connected to distribution of substance in any of channel’s arms and in entire channel. Obtained distributions are not discussed by other authors and can be connected to Waring distribution. Next, we discuss a model for flow of substance in a channel which arms contain finite number of nodes each. We obtain probability distributions connected to distribution of substance in the nodes of the channel for stationary regime of flow of substance. These distributions are also new and we calculate corresponding information measure and Shannon information measure for studied kind of flow of substance. Full article

(This article belongs to the Special Issue Condensed-Matter-Principia Based Information & Statistical Measures: From Classical to Quantum)

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21 pages, 1554 KiB

Open AccessArticle

Changes of Conformation in Albumin with Temperature by Molecular Dynamics Simulations

by Piotr Weber, Piotr Bełdowski, Krzysztof Domino, Damian Ledziński and Adam Gadomski

Entropy 2020, 22(4), 405; https://doi.org/10.3390/e22040405 - 1 Apr 2020

Cited by 5 | Viewed by 3426

Abstract

This work presents the analysis of the conformation of albumin in the temperature range of

300 K

–

312 K

, i.e., in the physiological range. Using molecular dynamics simulations, we calculate values of the backbone and dihedral angles for this molecule. We [...] Read more.

This work presents the analysis of the conformation of albumin in the temperature range of

300 K

–

312 K

, i.e., in the physiological range. Using molecular dynamics simulations, we calculate values of the backbone and dihedral angles for this molecule. We analyze the global dynamic properties of albumin treated as a chain. In this range of temperature, we study parameters of the molecule and the conformational entropy derived from two angles that reflect global dynamics in the conformational space. A thorough rationalization, based on the scaling theory, for the subdiffusion Flory–De Gennes type exponent of

0.4

unfolds in conjunction with picking up the most appreciable fluctuations of the corresponding statistical-test parameter. These fluctuations coincide adequately with entropy fluctuations, namely the oscillations out of thermodynamic equilibrium. Using Fisher’s test, we investigate the conformational entropy over time and suggest its oscillatory properties in the corresponding time domain. Using the Kruscal–Wallis test, we also analyze differences between the root mean square displacement of a molecule at various temperatures. Here we show that its values in the range of

306 K

–

309 K

are different than in another temperature. Using the Kullback–Leibler theory, we investigate differences between the distribution of the root mean square displacement for each temperature and time window. Full article

(This article belongs to the Special Issue Condensed-Matter-Principia Based Information & Statistical Measures: From Classical to Quantum)

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17 pages, 13800 KiB

Open AccessArticle

Applications of Information Theory Methods for Evolutionary Optimization of Chemical Computers

by Jerzy Gorecki

Entropy 2020, 22(3), 313; https://doi.org/10.3390/e22030313 - 10 Mar 2020

Cited by 9 | Viewed by 3206

Abstract

It is commonly believed that information processing in living organisms is based on chemical reactions. However, the human achievements in constructing chemical information processing devices demonstrate that it is difficult to design such devices using the bottom-up strategy. Here I discuss the alternative top-down design of a network of chemical oscillators that performs a selected computing task. As an example, I consider a simple network of interacting chemical oscillators that operates as a comparator of two real numbers. The information on which of the two numbers is larger is coded in the number of excitations observed on oscillators forming the network. The parameters of the network are optimized to perform this function with the maximum accuracy. I discuss how information theory methods can be applied to obtain the optimum computing structure. Full article

(This article belongs to the Special Issue Condensed-Matter-Principia Based Information & Statistical Measures: From Classical to Quantum)

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7 pages, 341 KiB

Open AccessArticle

Binary Communication with Gazeau–Klauder Coherent States

by Jerzy Dajka and Jerzy Łuczka

Entropy 2020, 22(2), 201; https://doi.org/10.3390/e22020201 - 10 Feb 2020

Cited by 4 | Viewed by 2337

Abstract

We investigate advantages and disadvantages of using Gazeau–Klauder coherent states for optical communication. In this short paper we show that using an alphabet consisting of coherent Gazeau–Klauder states related to a Kerr-type nonlinear oscillator instead of standard Perelomov coherent states results in lowering of the Helstrom bound for error probability in binary communication. We also discuss trace distance between Gazeau–Klauder coherent states and a standard coherent state as a quantifier of distinguishability of alphabets. Full article

(This article belongs to the Special Issue Condensed-Matter-Principia Based Information & Statistical Measures: From Classical to Quantum)

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11 pages, 1635 KiB

Open AccessArticle

Electromagnetically Induced Transparency in Media with Rydberg Excitons 1: Slow Light

by David Ziemkiewicz

Entropy 2020, 22(2), 177; https://doi.org/10.3390/e22020177 - 4 Feb 2020

Cited by 7 | Viewed by 2846

Abstract

In this paper, we show that Electromagnetically Induced Transparency (EIT) can be realized in mediums with Rydberg excitons. With realistic, reliable parameters which show good agreement with optical and electro-optical experiments, as well as the proper choice of Rydberg exciton states in the Cu₂O crystal, we indicate how the EIT can be performed. The calculations show that, due to a large group index, one can expect the slowing down of a light pulse by a factor of about

10^{4}

in this medium. Full article

(This article belongs to the Special Issue Condensed-Matter-Principia Based Information & Statistical Measures: From Classical to Quantum)

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10 pages, 839 KiB

Open AccessArticle

Electromagnetically Induced Transparency in Media with Rydberg Excitons 2: Cross-Kerr Modulation

by David Ziemkiewicz and Sylwia Zielińska - Raczyńska

Entropy 2020, 22(2), 160; https://doi.org/10.3390/e22020160 - 30 Jan 2020

Cited by 6 | Viewed by 2715

Abstract

By mapping photons into the sample of cuprous oxide with Rydberg excitons, it is possible to obtain a significant optical phase shift due to third-order cross-Kerr nonlinearities realized under the conditions of electromagnetically induced transparency. The optimum conditions for observation of the phase [...] Read more.

π

in Rydberg excitons media are examined. A discussion of the application of the cross-phase modulations in the field of all-optical quantum information processing in solid-state systems is presented. Full article

(This article belongs to the Special Issue Condensed-Matter-Principia Based Information & Statistical Measures: From Classical to Quantum)

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15 pages, 1646 KiB

Open AccessArticle

Interaction and Entanglement of a Pair of Quantum Emitters near a Nanoparticle: Analysis beyond Electric-Dipole Approximation

by Miriam Kosik and Karolina Słowik

Entropy 2020, 22(2), 135; https://doi.org/10.3390/e22020135 - 23 Jan 2020

Cited by 2 | Viewed by 3278

Abstract

In this paper, we study the collective effects which appear as a pair of quantum emitters is positioned in close vicinity to a plasmonic nanoparticle. These effects include multipole–multipole interaction and collective decay, the strengths and rates of which are modified by the presence of the nanoparticle. As a result, entanglement is generated between the quantum emitters, which survives in the stationary state. To evaluate these effects, we exploit the Green’s tensor-based quantization scheme in the Markovian limit, taking into account the corrections from light–matter coupling channels higher than the electric dipole. We find these higher-order channels to significantly influence the collective rates and degree of entanglement, and in particular, to qualitatively influence their spatial profiles. Our findings indicate that, apart from quantitatively modifying the results, the higher-order interaction channels may introduce asymmetry into the spatial distribution of the collective response. Full article

(This article belongs to the Special Issue Condensed-Matter-Principia Based Information & Statistical Measures: From Classical to Quantum)

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13 pages, 2599 KiB

Open AccessArticle

Fractal Plasmons on Cantor Set Thin Film

by David Ziemkiewicz, Karol Karpiński and Sylwia Zielińska-Raczyńska

Entropy 2019, 21(12), 1176; https://doi.org/10.3390/e21121176 - 29 Nov 2019

Cited by 2 | Viewed by 2624

Abstract

The propagation of surface plasmon–polaritons is investigated in a metallic, fractal-like structure based on Cantor set. The dynamic of plasmonic modes generating on the Cantor structure is discussed in the context of the setup geometry. The numerically obtained reflection spectra are analyzed with the box-counting method to obtain their dimension, which is shown to be dependent on the geometry of the plasmonic structure. The entropy of the structure is also calculated and shown to be proportional to the dimension. Presented analysis allows for extracting information about fractal plasmonic structure from the reflectance spectrum. Predictions regarding the experimental observation of discussed effects are presented. Full article

(This article belongs to the Special Issue Condensed-Matter-Principia Based Information & Statistical Measures: From Classical to Quantum)

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20 pages, 3050 KiB

Open AccessArticle

Entropy and Information Theory: Uses and Misuses

by Arieh Ben-Naim

Entropy 2019, 21(12), 1170; https://doi.org/10.3390/e21121170 - 29 Nov 2019

Cited by 16 | Viewed by 7865

Abstract

This article is about the profound misuses, misunderstanding, misinterpretations and misapplications of entropy, the Second Law of Thermodynamics and Information Theory. It is the story of the “Greatest Blunder Ever in the History of Science”. It is not about a single blunder admitted by a single person (e.g., Albert Einstein allegedly said in connection with the cosmological constant, that this was his greatest blunder), but rather a blunder of gargantuan proportions whose claws have permeated all branches of science; from thermodynamics, cosmology, biology, psychology, sociology and much more. Full article

(This article belongs to the Special Issue Condensed-Matter-Principia Based Information & Statistical Measures: From Classical to Quantum)

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