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

      editorial

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          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.

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

          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.
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            Applications of Information Theory Methods for Evolutionary Optimization of Chemical Computers

            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.
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              Changes of Conformation in Albumin with Temperature by Molecular Dynamics Simulations

              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.
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                Author and article information

                Journal
                Entropy (Basel)
                Entropy (Basel)
                entropy
                Entropy
                MDPI
                1099-4300
                10 June 2020
                June 2020
                : 22
                : 6
                : 645
                Affiliations
                [1 ]Institute of Mathematics and Physics (Group of Modeling of Physicochemical Processes), Faculty of Chemical Technology and Engineering, UTP University of Science and Technology, 85-796 Bydgoszcz, Poland
                [2 ]Institute of Mathematics and Physics (Group of Quantum Optics and Information), Faculty of Chemical Technology and Engineering, UTP University of Science and Technology, 85-796 Bydgoszcz, Poland; sziel@ 123456utp.edu.pl
                Author notes
                [* ]Correspondence: agad@ 123456utp.edu.pl ; Tel.: +48-523-408-697
                Author information
                https://orcid.org/0000-0002-8201-1736
                https://orcid.org/0000-0003-0889-2093
                Article
                entropy-22-00645
                10.3390/e22060645
                7517181
                3776bdbd-f994-4f25-b4c3-6782bb8fc996
                © 2020 by the authors.

                Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

                History
                : 06 June 2020
                : 09 June 2020
                Categories
                Editorial

                information,entropy,classical vs. quantum system,condensed matter,soft matter,complex systems

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