Entropy

18 pages, 733 KiB

Open AccessEditor’s ChoiceArticle

Dependency Structures in Cryptocurrency Market from High to Low Frequency

by Antonio Briola and Tomaso Aste

Entropy 2022, 24(11), 1548; https://doi.org/10.3390/e24111548 - 28 Oct 2022

Cited by 11 | Viewed by 3180

We investigate logarithmic price returns cross-correlations at different time horizons for a set of 25 liquid cryptocurrencies traded on the FTX digital currency exchange. We study how the structure of the Minimum Spanning Tree (MST) and the Triangulated Maximally Filtered Graph (TMFG) evolve [...] Read more.

We investigate logarithmic price returns cross-correlations at different time horizons for a set of 25 liquid cryptocurrencies traded on the FTX digital currency exchange. We study how the structure of the Minimum Spanning Tree (MST) and the Triangulated Maximally Filtered Graph (TMFG) evolve from high (15 s) to low (1 day) frequency time resolutions. For each horizon, we test the stability, statistical significance and economic meaningfulness of the networks. Results give a deep insight into the evolutionary process of the time dependent hierarchical organization of the system under analysis. A decrease in correlation between pairs of cryptocurrencies is observed for finer time sampling resolutions. A growing structure emerges for coarser ones, highlighting multiple changes in the hierarchical reference role played by mainstream cryptocurrencies. This effect is studied both in its pairwise realizations and intra-sector ones. Full article

(This article belongs to the Special Issue Recent Trends and Developments in Econophysics)

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18 pages, 381 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

An Overview on Irreversible Port-Hamiltonian Systems

by Hector Ramirez and Yann Le Gorrec

Entropy 2022, 24(10), 1478; https://doi.org/10.3390/e24101478 - 17 Oct 2022

Cited by 12 | Viewed by 3126

Abstract

A comprehensive overview of the irreversible port-Hamiltonian system’s formulation for finite and infinite dimensional systems defined on 1D spatial domains is provided in a unified manner. The irreversible port-Hamiltonian system formulation shows the extension of classical port-Hamiltonian system formulations to cope with irreversible [...] Read more.

A comprehensive overview of the irreversible port-Hamiltonian system’s formulation for finite and infinite dimensional systems defined on 1D spatial domains is provided in a unified manner. The irreversible port-Hamiltonian system formulation shows the extension of classical port-Hamiltonian system formulations to cope with irreversible thermodynamic systems for finite and infinite dimensional systems. This is achieved by including, in an explicit manner, the coupling between irreversible mechanical and thermal phenomena with the thermal domain as an energy-preserving and entropy-increasing operator. Similarly to Hamiltonian systems, this operator is skew-symmetric, guaranteeing energy conservation. To distinguish from Hamiltonian systems, the operator depends on co-state variables and is, hence, a nonlinear-function in the gradient of the total energy. This is what allows encoding the second law as a structural property of irreversible port-Hamiltonian systems. The formalism encompasses coupled thermo-mechanical systems and purely reversible or conservative systems as a particular case. This appears clearly when splitting the state space such that the entropy coordinate is separated from other state variables. Several examples have been used to illustrate the formalism, both for finite and infinite dimensional systems, and a discussion on ongoing and future studies is provided. Full article

(This article belongs to the Special Issue Geometric Structure of Thermodynamics: Theory and Applications)

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29 pages, 670 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

“Yet Once More”: The Double-Slit Experiment and Quantum Discontinuity

by Arkady Plotnitsky

Entropy 2022, 24(10), 1455; https://doi.org/10.3390/e24101455 - 12 Oct 2022

Cited by 6 | Viewed by 2965

Abstract

This article reconsiders the double-slit experiment from the nonrealist or, in terms of this article, “reality-without-realism” (RWR) perspective, grounded in the combination of three forms of quantum discontinuity: (1) “Heisenberg discontinuity”, defined by the impossibility of a representation or even conception of how [...] Read more.

This article reconsiders the double-slit experiment from the nonrealist or, in terms of this article, “reality-without-realism” (RWR) perspective, grounded in the combination of three forms of quantum discontinuity: (1) “Heisenberg discontinuity”, defined by the impossibility of a representation or even conception of how quantum phenomena come about, even though quantum theory (such as quantum mechanics or quantum field theory) predicts the data in question strictly in accord with what is observed in quantum experiments); (2) “Bohr discontinuity”, defined, under the assumption of Heisenberg discontinuity, by the view that quantum phenomena and the data observed therein are described by classical and not quantum theory, even though classical physics cannot predict them; and (3) “Dirac discontinuity” (not considered by Dirac himself, but suggested by his equation), according to which the concept of a quantum object, such as a photon or electron, is an idealization only applicable at the time of observation and not to something that exists independently in nature. Dirac discontinuity is of particular importance for the article’s foundational argument and its analysis of the double-slit experiment. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering)

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17 pages, 399 KiB

Open AccessEditor’s ChoiceArticle

Information Theory for Biological Sequence Classification: A Novel Feature Extraction Technique Based on Tsallis Entropy

by Robson P. Bonidia, Anderson P. Avila Santos, Breno L. S. de Almeida, Peter F. Stadler, Ulisses Nunes da Rocha, Danilo S. Sanches and André C. P. L. F. de Carvalho

Entropy 2022, 24(10), 1398; https://doi.org/10.3390/e24101398 - 1 Oct 2022

Cited by 3 | Viewed by 3087

Abstract

In recent years, there has been an exponential growth in sequencing projects due to accelerated technological advances, leading to a significant increase in the amount of data and resulting in new challenges for biological sequence analysis. Consequently, the use of techniques capable of [...] Read more.

In recent years, there has been an exponential growth in sequencing projects due to accelerated technological advances, leading to a significant increase in the amount of data and resulting in new challenges for biological sequence analysis. Consequently, the use of techniques capable of analyzing large amounts of data has been explored, such as machine learning (ML) algorithms. ML algorithms are being used to analyze and classify biological sequences, despite the intrinsic difficulty in extracting and finding representative biological sequence methods suitable for them. Thereby, extracting numerical features to represent sequences makes it statistically feasible to use universal concepts from Information Theory, such as Tsallis and Shannon entropy. In this study, we propose a novel Tsallis entropy-based feature extractor to provide useful information to classify biological sequences. To assess its relevance, we prepared five case studies: (1) an analysis of the entropic index q; (2) performance testing of the best entropic indices on new datasets; (3) a comparison made with Shannon entropy and (4) generalized entropies; (5) an investigation of the Tsallis entropy in the context of dimensionality reduction. As a result, our proposal proved to be effective, being superior to Shannon entropy and robust in terms of generalization, and also potentially representative for collecting information in fewer dimensions compared with methods such as Singular Value Decomposition and Uniform Manifold Approximation and Projection. Full article

(This article belongs to the Special Issue Information Theory in Computational Biology)

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35 pages, 988 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Revisiting Chernoff Information with Likelihood Ratio Exponential Families

by Frank Nielsen

Entropy 2022, 24(10), 1400; https://doi.org/10.3390/e24101400 - 1 Oct 2022

Cited by 12 | Viewed by 5877

Abstract

The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance. Although the Chernoff information was originally introduced for bounding the Bayes error in statistical hypothesis testing, the divergence found many other applications [...] Read more.

The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance. Although the Chernoff information was originally introduced for bounding the Bayes error in statistical hypothesis testing, the divergence found many other applications due to its empirical robustness property found in applications ranging from information fusion to quantum information. From the viewpoint of information theory, the Chernoff information can also be interpreted as a minmax symmetrization of the Kullback–Leibler divergence. In this paper, we first revisit the Chernoff information between two densities of a measurable Lebesgue space by considering the exponential families induced by their geometric mixtures: The so-called likelihood ratio exponential families. Second, we show how to (i) solve exactly the Chernoff information between any two univariate Gaussian distributions or get a closed-form formula using symbolic computing, (ii) report a closed-form formula of the Chernoff information of centered Gaussians with scaled covariance matrices and (iii) use a fast numerical scheme to approximate the Chernoff information between any two multivariate Gaussian distributions. Full article

(This article belongs to the Special Issue Robust Distance Metric Learning in the Framework of Statistical Information Theory)

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22 pages, 560 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

On Quantum Entropy

by Davi Geiger and Zvi M. Kedem

Entropy 2022, 24(10), 1341; https://doi.org/10.3390/e24101341 - 23 Sep 2022

Cited by 5 | Viewed by 6361

Abstract

Quantum physics, despite its intrinsically probabilistic nature, lacks a definition of entropy fully accounting for the randomness of a quantum state. For example, von Neumann entropy quantifies only the incomplete specification of a quantum state and does not quantify the probabilistic distribution of [...] Read more.

Quantum physics, despite its intrinsically probabilistic nature, lacks a definition of entropy fully accounting for the randomness of a quantum state. For example, von Neumann entropy quantifies only the incomplete specification of a quantum state and does not quantify the probabilistic distribution of its observables; it trivially vanishes for pure quantum states. We propose a quantum entropy that quantifies the randomness of a pure quantum state via a conjugate pair of observables/operators forming the quantum phase space. The entropy is dimensionless, it is a relativistic scalar, it is invariant under canonical transformations and under CPT transformations, and its minimum has been established by the entropic uncertainty principle. We expand the entropy to also include mixed states. We show that the entropy is monotonically increasing during a time evolution of coherent states under a Dirac Hamiltonian. However, in a mathematical scenario, when two fermions come closer to each other, each evolving as a coherent state, the total system’s entropy oscillates due to the increasing spatial entanglement. We hypothesize an entropy law governing physical systems whereby the entropy of a closed system never decreases, implying a time arrow for particle physics. We then explore the possibility that as the oscillations of the entropy must by the law be barred in quantum physics, potential entropy oscillations trigger annihilation and creation of particles. Full article

(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)

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30 pages, 633 KiB

Open AccessEditor’s ChoiceArticle

Assessing, Testing and Estimating the Amount of Fine-Tuning by Means of Active Information

by Daniel Andrés Díaz-Pachón and Ola Hössjer

Entropy 2022, 24(10), 1323; https://doi.org/10.3390/e24101323 - 21 Sep 2022

Cited by 9 | Viewed by 2271

Abstract

A general framework is introduced to estimate how much external information has been infused into a search algorithm, the so-called active information. This is rephrased as a test of fine-tuning, where tuning corresponds to the amount of pre-specified knowledge that the algorithm makes [...] Read more.

A general framework is introduced to estimate how much external information has been infused into a search algorithm, the so-called active information. This is rephrased as a test of fine-tuning, where tuning corresponds to the amount of pre-specified knowledge that the algorithm makes use of in order to reach a certain target. A function f quantifies specificity for each possible outcome x of a search, so that the target of the algorithm is a set of highly specified states, whereas fine-tuning occurs if it is much more likely for the algorithm to reach the target as intended than by chance. The distribution of a random outcome X of the algorithm involves a parameter

θ

that quantifies how much background information has been infused. A simple choice of this parameter is to use

θ f

in order to exponentially tilt the distribution of the outcome of the search algorithm under the null distribution of no tuning, so that an exponential family of distributions is obtained. Such algorithms are obtained by iterating a Metropolis–Hastings type of Markov chain, which makes it possible to compute their active information under the equilibrium and non-equilibrium of the Markov chain, with or without stopping when the targeted set of fine-tuned states has been reached. Other choices of tuning parameters

θ

are discussed as well. Nonparametric and parametric estimators of active information and tests of fine-tuning are developed when repeated and independent outcomes of the algorithm are available. The theory is illustrated with examples from cosmology, student learning, reinforcement learning, a Moran type model of population genetics, and evolutionary programming. Full article

(This article belongs to the Special Issue Recent Advances in Statistical Theory and Applications)

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10 pages, 2358 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Statistical Mechanics of Political Polarization

by Miron Kaufman, Sanda Kaufman and Hung T. Diep

Entropy 2022, 24(9), 1262; https://doi.org/10.3390/e24091262 - 8 Sep 2022

Cited by 10 | Viewed by 5098

Abstract

Rapidly increasing political polarization threatens democracies around the world. Scholars from several disciplines are assessing and modeling polarization antecedents, processes, and consequences. Social systems are complex and networked. Their constant shifting hinders attempts to trace causes of observed trends, predict their consequences, or [...] Read more.

Rapidly increasing political polarization threatens democracies around the world. Scholars from several disciplines are assessing and modeling polarization antecedents, processes, and consequences. Social systems are complex and networked. Their constant shifting hinders attempts to trace causes of observed trends, predict their consequences, or mitigate them. We propose an equivalent-neighbor model of polarization dynamics. Using statistical physics techniques, we generate anticipatory scenarios and examine whether leadership and/or external events alleviate or exacerbate polarization. We consider three highly polarized USA groups: Democrats, Republicans, and Independents. We assume that in each group, each individual has a political stance s ranging between left and right. We quantify the noise in this system as a “social temperature” T. Using energy E, we describe individuals’ interactions in time within their own group and with individuals of the other groups. It depends on the stance s as well as on three intra-group and six inter-group coupling parameters. We compute the probability distributions of stances at any time using the Boltzmann probability weight exp(−E/T). We generate average group-stance scenarios in time and explore whether concerted interventions or unexpected shocks can alter them. The results inform on the perils of continuing the current polarization trends, as well as on possibilities of changing course. Full article

(This article belongs to the Special Issue Statistical Physics of Opinion Formation and Social Phenomena)

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17 pages, 4479 KiB

Open AccessEditor’s ChoiceArticle

Elastic Entropic Forces in Polymer Deformation

by Vladimir I. Kartsovnik and Dimitri Volchenkov

Entropy 2022, 24(9), 1260; https://doi.org/10.3390/e24091260 - 7 Sep 2022

Cited by 9 | Viewed by 3582

Abstract

The entropic nature of elasticity of long molecular chains and reticulated materials is discussed concerning the analysis of flows of polymer melts and elastomer deformation in the framework of Frenkel–Eyring molecular kinetic theory. Deformation curves are calculated in line with the simple viscoelasticity [...] Read more.

The entropic nature of elasticity of long molecular chains and reticulated materials is discussed concerning the analysis of flows of polymer melts and elastomer deformation in the framework of Frenkel–Eyring molecular kinetic theory. Deformation curves are calculated in line with the simple viscoelasticity models where the activation energy of viscous flow depends on the magnitude of elastic entropic forces of the stretched macromolecules. The interconnections between deformation processes and the structure of elastomer networks, as well as their mutual influence on each other, are considered. Full article

(This article belongs to the Special Issue Entropic Forces in Complex Systems II)

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Graphical abstract

11 pages, 1415 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Decoding ‘Maximum Entropy’ Deconvolution

by Long V. Le, Tae Jung Kim, Young Dong Kim and David E. Aspnes

Entropy 2022, 24(9), 1238; https://doi.org/10.3390/e24091238 - 2 Sep 2022

Cited by 6 | Viewed by 4918

Abstract

For over five decades, the mathematical procedure termed “maximum entropy” (M-E) has been used to deconvolve structure in spectra, optical and otherwise, although quantitative measures of performance remain unknown. Here, we examine this procedure analytically for the lowest two orders for a Lorentzian [...] Read more.

For over five decades, the mathematical procedure termed “maximum entropy” (M-E) has been used to deconvolve structure in spectra, optical and otherwise, although quantitative measures of performance remain unknown. Here, we examine this procedure analytically for the lowest two orders for a Lorentzian feature, obtaining expressions for the amount of sharpening and identifying how spurious structures appear. Illustrative examples are provided. These results enhance the utility of this widely used deconvolution approach to spectral analysis. Full article

(This article belongs to the Special Issue Concepts of Entropy and Their Applications III)

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15 pages, 1850 KiB

Open AccessEditor’s ChoiceArticle

A Bayesian Analysis of Plant DNA Length Distribution via κ-Statistics

by Maxsuel M. F. de Lima, Dory H. A. L. Anselmo, Raimundo Silva, Glauber H. S. Nunes, Umberto L. Fulco, Manoel S. Vasconcelos and Vamberto D. Mello

Entropy 2022, 24(9), 1225; https://doi.org/10.3390/e24091225 - 1 Sep 2022

Cited by 6 | Viewed by 2019

Abstract

We report an analysis of the distribution of lengths of plant DNA (exons). Three species of Cucurbitaceae were investigated. In our study, we used two distinct

κ

distribution functions, namely,

κ

-Maxwellian and double-

κ

, to fit the length distributions. To determine [...] Read more.

We report an analysis of the distribution of lengths of plant DNA (exons). Three species of Cucurbitaceae were investigated. In our study, we used two distinct

κ

distribution functions, namely,

κ

-Maxwellian and double-

κ

, to fit the length distributions. To determine which distribution has the best fitting, we made a Bayesian analysis of the models. Furthermore, we filtered the data, removing outliers, through a box plot analysis. Our findings show that the sum of

κ

-exponentials is the most appropriate to adjust the distribution curves and that the values of the

κ

parameter do not undergo considerable changes after filtering. Furthermore, for the analyzed species, there is a tendency for the

κ

parameter to lay within the interval

(0.27; 0.43)

. Full article

(This article belongs to the Special Issue Twenty Years of Kaniadakis Entropy: Current Trends and Future Perspectives)

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22 pages, 446 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Efficiency of the Moscow Stock Exchange before 2022

by Andrey Shternshis, Piero Mazzarisi and Stefano Marmi

Entropy 2022, 24(9), 1184; https://doi.org/10.3390/e24091184 - 25 Aug 2022

Cited by 7 | Viewed by 3081

Abstract

This paper investigates the degree of efficiency for the Moscow Stock Exchange. A market is called efficient if prices of its assets fully reflect all available information. We show that the degree of market efficiency is significantly low for most of the months [...] Read more.

This paper investigates the degree of efficiency for the Moscow Stock Exchange. A market is called efficient if prices of its assets fully reflect all available information. We show that the degree of market efficiency is significantly low for most of the months from 2012 to 2021. We calculate the degree of market efficiency by (i) filtering out regularities in financial data and (ii) computing the Shannon entropy of the filtered return time series. We developed a simple method for estimating volatility and price staleness in empirical data in order to filter out such regularity patterns from return time series. The resulting financial time series of stock returns are then clustered into different groups according to some entropy measures. In particular, we use the Kullback–Leibler distance and a novel entropy metric capturing the co-movements between pairs of stocks. By using Monte Carlo simulations, we are then able to identify the time periods of market inefficiency for a group of 18 stocks. The inefficiency of the Moscow Stock Exchange that we have detected is a signal of the possibility of devising profitable strategies, net of transaction costs. The deviation from the efficient behavior for a stock strongly depends on the industrial sector that it belongs to. Full article

(This article belongs to the Special Issue Applications of Statistical Physics in Finance and Economics)

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19 pages, 5449 KiB

Open AccessEditor’s ChoiceArticle

Monte Carlo Simulation of Stochastic Differential Equation to Study Information Geometry

by Abhiram Anand Thiruthummal and Eun-jin Kim

Entropy 2022, 24(8), 1113; https://doi.org/10.3390/e24081113 - 12 Aug 2022

Cited by 9 | Viewed by 3029

Abstract

Information Geometry is a useful tool to study and compare the solutions of a Stochastic Differential Equations (SDEs) for non-equilibrium systems. As an alternative method to solving the Fokker–Planck equation, we propose a new method to calculate time-dependent probability density functions (PDFs) and [...] Read more.

Information Geometry is a useful tool to study and compare the solutions of a Stochastic Differential Equations (SDEs) for non-equilibrium systems. As an alternative method to solving the Fokker–Planck equation, we propose a new method to calculate time-dependent probability density functions (PDFs) and to study Information Geometry using Monte Carlo (MC) simulation of SDEs. Specifically, we develop a new MC SDE method to overcome the challenges in calculating a time-dependent PDF and information geometric diagnostics and to speed up simulations by utilizing GPU computing. Using MC SDE simulations, we reproduce Information Geometric scaling relations found from the Fokker–Planck method for the case of a stochastic process with linear and cubic damping terms. We showcase the advantage of MC SDE simulation over FPE solvers by calculating unequal time joint PDFs. For the linear process with a linear damping force, joint PDF is found to be a Gaussian. In contrast, for the cubic process with a cubic damping force, joint PDF exhibits a bimodal structure, even in a stationary state. This suggests a finite memory time induced by a nonlinear force. Furthermore, several power-law scalings in the characteristics of bimodal PDFs are identified and investigated. Full article

(This article belongs to the Special Issue Entropies, Information Geometry and Fluctuations in Non-equilibrium Systems)

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16 pages, 5801 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Pseudoclassical Dynamics of the Kicked Top

by Zhixing Zou and Jiao Wang

Entropy 2022, 24(8), 1092; https://doi.org/10.3390/e24081092 - 9 Aug 2022

Cited by 4 | Viewed by 2784

Abstract

The kicked rotor and the kicked top are two paradigms of quantum chaos. The notions of quantum resonance and the pseudoclassical limit, developed in the study of the kicked rotor, have revealed an intriguing and unconventional aspect of classical–quantum correspondence. Here, we show [...] Read more.

The kicked rotor and the kicked top are two paradigms of quantum chaos. The notions of quantum resonance and the pseudoclassical limit, developed in the study of the kicked rotor, have revealed an intriguing and unconventional aspect of classical–quantum correspondence. Here, we show that, by extending these notions to the kicked top, its rich dynamical behavior can be appreciated more thoroughly; of special interest is the entanglement entropy. In particular, the periodic synchronization between systems subject to different kicking strength can be conveniently understood and elaborated from the pseudoclassical perspective. The applicability of the suggested general pseudoclassical theory to the kicked rotor is also discussed. Full article

(This article belongs to the Special Issue Quantum Chaos—Dedicated to Professor Giulio Casati on the Occasion of His 80th Birthday)

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25 pages, 409 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Information Theoretic Methods for Variable Selection—A Review

by Jan Mielniczuk

Entropy 2022, 24(8), 1079; https://doi.org/10.3390/e24081079 - 4 Aug 2022

Cited by 7 | Viewed by 2943

Abstract

We review the principal information theoretic tools and their use for feature selection, with the main emphasis on classification problems with discrete features. Since it is known that empirical versions of conditional mutual information perform poorly for high-dimensional problems, we focus on various [...] Read more.

We review the principal information theoretic tools and their use for feature selection, with the main emphasis on classification problems with discrete features. Since it is known that empirical versions of conditional mutual information perform poorly for high-dimensional problems, we focus on various ways of constructing its counterparts and the properties and limitations of such methods. We present a unified way of constructing such measures based on truncation, or truncation and weighing, for the Möbius expansion of conditional mutual information. We also discuss the main approaches to feature selection which apply the introduced measures of conditional dependence, together with the ways of assessing the quality of the obtained vector of predictors. This involves discussion of recent results on asymptotic distributions of empirical counterparts of criteria, as well as advances in resampling. Full article

(This article belongs to the Special Issue Information Theoretic Criteria: New Theoretical Developments and Applications)

6 pages, 255 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Memory and Entropy

by Carlo Rovelli

Entropy 2022, 24(8), 1022; https://doi.org/10.3390/e24081022 - 24 Jul 2022

Cited by 16 | Viewed by 5930

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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11 pages, 4222 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Critical Quantum Metrology in the Non-Linear Quantum Rabi Model

by Zu-Jian Ying, Simone Felicetti, Gang Liu and Daniel Braak

Entropy 2022, 24(8), 1015; https://doi.org/10.3390/e24081015 - 22 Jul 2022

Cited by 33 | Viewed by 3228

Abstract

The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear [...] Read more.

The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms. Full article

(This article belongs to the Special Issue Current Trends in Quantum Phase Transitions)

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15 pages, 14830 KiB

Open AccessEditor’s ChoiceArticle

Consensus, Polarization and Hysteresis in the Three-State Noisy q-Voter Model with Bounded Confidence

by Maciej Doniec, Arkadiusz Lipiecki and Katarzyna Sznajd-Weron

Entropy 2022, 24(7), 983; https://doi.org/10.3390/e24070983 - 16 Jul 2022

Cited by 12 | Viewed by 2530

Abstract

In this work, we address the question of the role of the influence of group size on the emergence of various collective social phenomena, such as consensus, polarization and social hysteresis. To answer this question, we study the three-state noisy q-voter model [...] Read more.

In this work, we address the question of the role of the influence of group size on the emergence of various collective social phenomena, such as consensus, polarization and social hysteresis. To answer this question, we study the three-state noisy q-voter model with bounded confidence, in which agents can be in one of three states: two extremes (leftist and rightist) and centrist. We study the model on a complete graph within the mean-field approach and show that, depending on the size q of the influence group, saddle-node bifurcation cascades of different length appear and different collective phenomena are possible. In particular, for all values of

q > 1

, social hysteresis is observed. Furthermore, for small values of

q \in (1, 4)

, disagreement, polarization and domination of centrists (a consensus understood as the general agreement, not unanimity) can be achieved but not the domination of extremists. The latter is possible only for larger groups of influence. Finally, by comparing our model to others, we discuss how a small change in the rules at the microscopic level can dramatically change the macroscopic behavior of the model. Full article

(This article belongs to the Special Issue Modern Trends in Sociophysics)

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19 pages, 2088 KiB

Open AccessFeature PaperEditor’s ChoiceReview

Revealing the Dynamics of Neural Information Processing with Multivariate Information Decomposition

by Ehren L. Newman, Thomas F. Varley, Vibin K. Parakkattu, Samantha P. Sherrill and John M. Beggs

Entropy 2022, 24(7), 930; https://doi.org/10.3390/e24070930 - 5 Jul 2022

Cited by 20 | Viewed by 5003

Abstract

The varied cognitive abilities and rich adaptive behaviors enabled by the animal nervous system are often described in terms of information processing. This framing raises the issue of how biological neural circuits actually process information, and some of the most fundamental outstanding questions [...] Read more.

The varied cognitive abilities and rich adaptive behaviors enabled by the animal nervous system are often described in terms of information processing. This framing raises the issue of how biological neural circuits actually process information, and some of the most fundamental outstanding questions in neuroscience center on understanding the mechanisms of neural information processing. Classical information theory has long been understood to be a natural framework within which information processing can be understood, and recent advances in the field of multivariate information theory offer new insights into the structure of computation in complex systems. In this review, we provide an introduction to the conceptual and practical issues associated with using multivariate information theory to analyze information processing in neural circuits, as well as discussing recent empirical work in this vein. Specifically, we provide an accessible introduction to the partial information decomposition (PID) framework. PID reveals redundant, unique, and synergistic modes by which neurons integrate information from multiple sources. We focus particularly on the synergistic mode, which quantifies the “higher-order” information carried in the patterns of multiple inputs and is not reducible to input from any single source. Recent work in a variety of model systems has revealed that synergistic dynamics are ubiquitous in neural circuitry and show reliable structure–function relationships, emerging disproportionately in neuronal rich clubs, downstream of recurrent connectivity, and in the convergence of correlated activity. We draw on the existing literature on higher-order information dynamics in neuronal networks to illustrate the insights that have been gained by taking an information decomposition perspective on neural activity. Finally, we briefly discuss future promising directions for information decomposition approaches to neuroscience, such as work on behaving animals, multi-target generalizations of PID, and time-resolved local analyses. Full article

(This article belongs to the Special Issue Information Theory in Computational Biology)

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32 pages, 18172 KiB

Open AccessEditor’s ChoiceArticle

Causal Inference in Time Series in Terms of Rényi Transfer Entropy

by Petr Jizba, Hynek Lavička and Zlata Tabachová

Entropy 2022, 24(7), 855; https://doi.org/10.3390/e24070855 - 22 Jun 2022

Cited by 12 | Viewed by 5051

Abstract

Uncovering causal interdependencies from observational data is one of the great challenges of a nonlinear time series analysis. In this paper, we discuss this topic with the help of an information-theoretic concept known as Rényi’s information measure. In particular, we tackle the directional [...] Read more.

Uncovering causal interdependencies from observational data is one of the great challenges of a nonlinear time series analysis. In this paper, we discuss this topic with the help of an information-theoretic concept known as Rényi’s information measure. In particular, we tackle the directional information flow between bivariate time series in terms of Rényi’s transfer entropy. We show that by choosing Rényi’s parameter

α

, we can appropriately control information that is transferred only between selected parts of the underlying distributions. This, in turn, is a particularly potent tool for quantifying causal interdependencies in time series, where the knowledge of “black swan” events, such as spikes or sudden jumps, are of key importance. In this connection, we first prove that for Gaussian variables, Granger causality and Rényi transfer entropy are entirely equivalent. Moreover, we also partially extend these results to heavy-tailed

α

-Gaussian variables. These results allow establishing a connection between autoregressive and Rényi entropy-based information-theoretic approaches to data-driven causal inference. To aid our intuition, we employed the Leonenko et al. entropy estimator and analyzed Rényi’s information flow between bivariate time series generated from two unidirectionally coupled Rössler systems. Notably, we find that Rényi’s transfer entropy not only allows us to detect a threshold of synchronization but it also provides non-trivial insight into the structure of a transient regime that exists between the region of chaotic correlations and synchronization threshold. In addition, from Rényi’s transfer entropy, we could reliably infer the direction of coupling and, hence, causality, only for coupling strengths smaller than the onset value of the transient regime, i.e., when two Rössler systems are coupled but have not yet entered synchronization. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)

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14 pages, 471 KiB

Open AccessEditor’s ChoiceArticle

Multi-User Measurement-Device-Independent Quantum Key Distribution Based on GHZ Entangled State

by Ximing Hua, Min Hu and Banghong Guo

Entropy 2022, 24(6), 841; https://doi.org/10.3390/e24060841 - 18 Jun 2022

Cited by 11 | Viewed by 3019

Abstract

As a multi-particle entangled state, the Greenberger–Horne–Zeilinger (GHZ) state plays an important role in quantum theory and applications. In this study, we propose a flexible multi-user measurement-device-independent quantum key distribution (MDI-QKD) scheme based on a GHZ entangled state. Our scheme can distribute quantum [...] Read more.

As a multi-particle entangled state, the Greenberger–Horne–Zeilinger (GHZ) state plays an important role in quantum theory and applications. In this study, we propose a flexible multi-user measurement-device-independent quantum key distribution (MDI-QKD) scheme based on a GHZ entangled state. Our scheme can distribute quantum keys among multiple users while being resistant to detection attacks. Our simulation results show that the secure distance between each user and the measurement device can reach more than 280 km while reducing the complexity of the quantum network. Additionally, we propose a method to expand our scheme to a multi-node with multi-user network, which can further enhance the communication distance between the users at different nodes. Full article

(This article belongs to the Special Issue Quantum Information and Computation)

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28 pages, 1093 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Effective Field Theory of Random Quantum Circuits

by Yunxiang Liao and Victor Galitski

Entropy 2022, 24(6), 823; https://doi.org/10.3390/e24060823 - 13 Jun 2022

Cited by 4 | Viewed by 3390

Abstract

Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy [...] Read more.

Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems. Full article

(This article belongs to the Special Issue Quantum Chaos—Dedicated to Professor Giulio Casati on the Occasion of His 80th Birthday)

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17 pages, 443 KiB

Open AccessEditor’s ChoiceArticle

Quantum Non-Markovian Environment-to-System Backflows of Information: Nonoperational vs. Operational Approaches

by Adrián A. Budini

Entropy 2022, 24(5), 649; https://doi.org/10.3390/e24050649 - 5 May 2022

Cited by 10 | Viewed by 2214

Abstract

Quantum memory effects can be qualitatively understood as a consequence of an environment-to-system backflow of information. Here, we analyze and compare how this concept is interpreted and implemented in different approaches to quantum non-Markovianity. We study a nonoperational approach, defined by the distinguishability [...] Read more.

Quantum memory effects can be qualitatively understood as a consequence of an environment-to-system backflow of information. Here, we analyze and compare how this concept is interpreted and implemented in different approaches to quantum non-Markovianity. We study a nonoperational approach, defined by the distinguishability between two system states characterized by different initial conditions, and an operational approach, which is defined by the correlation between different outcomes associated to successive measurement processes performed over the system of interest. The differences, limitations, and vantages of each approach are characterized in detail by considering diverse system–environment models and dynamics. As a specific example, we study a non-Markovian depolarizing map induced by the interaction of the system of interest with an environment characterized by incoherent and coherent self-dynamics. Full article

(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)

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44 pages, 2198 KiB

Open AccessEditor’s ChoiceArticle

Entropy and the Experience of Heat

by Hans U. Fuchs, Michele D’Anna and Federico Corni

Entropy 2022, 24(5), 646; https://doi.org/10.3390/e24050646 - 4 May 2022

Cited by 13 | Viewed by 4083

Abstract

We discuss how to construct a direct and experientially natural path to entropy as a extensive quantity of a macroscopic theory of thermal systems and processes. The scientific aspects of this approach are based upon continuum thermodynamics. We ask what the roots of [...] Read more.

We discuss how to construct a direct and experientially natural path to entropy as a extensive quantity of a macroscopic theory of thermal systems and processes. The scientific aspects of this approach are based upon continuum thermodynamics. We ask what the roots of an experientially natural approach might be—to this end we investigate and describe in some detail (a) how humans experience and conceptualize an extensive thermal quantity (i.e., an amount of heat), and (b) how this concept evolved during the early development of the science of thermal phenomena (beginning with the Experimenters of the Accademia del Cimento and ending with Sadi Carnot). We show that a direct approach to entropy, as the extensive quantity of models of thermal systems and processes, is possible and how it can be applied to the teaching of thermodynamics for various audiences. Full article

(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)

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32 pages, 10388 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

The Cross-Sectional Intrinsic Entropy—A Comprehensive Stock Market Volatility Estimator

by Claudiu Vințe and Marcel Ausloos

Entropy 2022, 24(5), 623; https://doi.org/10.3390/e24050623 - 29 Apr 2022

Cited by 4 | Viewed by 4258

Abstract

To take into account the temporal dimension of uncertainty in stock markets, this paper introduces a cross-sectional estimation of stock market volatility based on the intrinsic entropy model. The proposed cross-sectional intrinsic entropy (CSIE) is defined and computed as a daily [...] Read more.

To take into account the temporal dimension of uncertainty in stock markets, this paper introduces a cross-sectional estimation of stock market volatility based on the intrinsic entropy model. The proposed cross-sectional intrinsic entropy (CSIE) is defined and computed as a daily volatility estimate for the entire market, grounded on the daily traded prices—open, high, low, and close prices (OHLC)—along with the daily traded volume for all symbols listed on The New York Stock Exchange (NYSE) and The National Association of Securities Dealers Automated Quotations (NASDAQ). We perform a comparative analysis between the time series obtained from the CSIE and the historical volatility as provided by the estimators: close-to-close, Parkinson, Garman–Klass, Rogers–Satchell, Yang–Zhang, and intrinsic entropy (IE), defined and computed from historical OHLC daily prices of the Standard & Poor’s 500 index (S&P500), Dow Jones Industrial Average (DJIA), and the NASDAQ Composite index, respectively, for various time intervals. Our study uses an approximate 6000-day reference point, starting 1 January 2001, until 23 January 2022, for both the NYSE and the NASDAQ. We found that the CSIE market volatility estimator is consistently at least 10 times more sensitive to market changes, compared to the volatility estimate captured through the market indices. Furthermore, beta values confirm a consistently lower volatility risk for market indices overall, between 50% and 90% lower, compared to the volatility risk of the entire market in various time intervals and rolling windows. Full article

(This article belongs to the Special Issue Fractal and Multifractal Analysis of Complex Networks)

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28 pages, 514 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Robust Test Statistics Based on Restricted Minimum Rényi’s Pseudodistance Estimators

by María Jaenada, Pedro Miranda and Leandro Pardo

Entropy 2022, 24(5), 616; https://doi.org/10.3390/e24050616 - 28 Apr 2022

Cited by 8 | Viewed by 2201

Abstract

The Rao’s score, Wald and likelihood ratio tests are the most common procedures for testing hypotheses in parametric models. None of the three test statistics is uniformly superior to the other two in relation with the power function, and moreover, they are first-order [...] Read more.

The Rao’s score, Wald and likelihood ratio tests are the most common procedures for testing hypotheses in parametric models. None of the three test statistics is uniformly superior to the other two in relation with the power function, and moreover, they are first-order equivalent and asymptotically optimal. Conversely, these three classical tests present serious robustness problems, as they are based on the maximum likelihood estimator, which is highly non-robust. To overcome this drawback, some test statistics have been introduced in the literature based on robust estimators, such as robust generalized Wald-type and Rao-type tests based on minimum divergence estimators. In this paper, restricted minimum Rényi’s pseudodistance estimators are defined, and their asymptotic distribution and influence function are derived. Further, robust Rao-type and divergence-based tests based on minimum Rényi’s pseudodistance and restricted minimum Rényi’s pseudodistance estimators are considered, and the asymptotic properties of the new families of tests statistics are obtained. Finally, the robustness of the proposed estimators and test statistics is empirically examined through a simulation study, and illustrative applications in real-life data are analyzed. Full article

(This article belongs to the Special Issue Information and Divergence Measures)

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26 pages, 2272 KiB

Open AccessEditor’s ChoiceArticle

Metacognition as a Consequence of Competing Evolutionary Time Scales

by Franz Kuchling, Chris Fields and Michael Levin

Entropy 2022, 24(5), 601; https://doi.org/10.3390/e24050601 - 26 Apr 2022

Cited by 21 | Viewed by 8757

Abstract

Evolution is full of coevolving systems characterized by complex spatio-temporal interactions that lead to intertwined processes of adaptation. Yet, how adaptation across multiple levels of temporal scales and biological complexity is achieved remains unclear. Here, we formalize how evolutionary multi-scale processing underlying adaptation [...] Read more.

Evolution is full of coevolving systems characterized by complex spatio-temporal interactions that lead to intertwined processes of adaptation. Yet, how adaptation across multiple levels of temporal scales and biological complexity is achieved remains unclear. Here, we formalize how evolutionary multi-scale processing underlying adaptation constitutes a form of metacognition flowing from definitions of metaprocessing in machine learning. We show (1) how the evolution of metacognitive systems can be expected when fitness landscapes vary on multiple time scales, and (2) how multiple time scales emerge during coevolutionary processes of sufficiently complex interactions. After defining a metaprocessor as a regulator with local memory, we prove that metacognition is more energetically efficient than purely object-level cognition when selection operates at multiple timescales in evolution. Furthermore, we show that existing modeling approaches to coadaptation and coevolution—here active inference networks, predator–prey interactions, coupled genetic algorithms, and generative adversarial networks—lead to multiple emergent timescales underlying forms of metacognition. Lastly, we show how coarse-grained structures emerge naturally in any resource-limited system, providing sufficient evidence for metacognitive systems to be a prevalent and vital component of (co-)evolution. Therefore, multi-scale processing is a necessary requirement for many evolutionary scenarios, leading to de facto metacognitive evolutionary outcomes. Full article

(This article belongs to the Special Issue Towards a Quantitative Understanding of Agency)

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31 pages, 469 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Information Inequalities via Submodularity and a Problem in Extremal Graph Theory

by Igal Sason

Entropy 2022, 24(5), 597; https://doi.org/10.3390/e24050597 - 25 Apr 2022

Cited by 4 | Viewed by 3416

Abstract

The present paper offers, in its first part, a unified approach for the derivation of families of inequalities for set functions which satisfy sub/supermodularity properties. It applies this approach for the derivation of information inequalities with Shannon information measures. Connections of the considered [...] Read more.

The present paper offers, in its first part, a unified approach for the derivation of families of inequalities for set functions which satisfy sub/supermodularity properties. It applies this approach for the derivation of information inequalities with Shannon information measures. Connections of the considered approach to a generalized version of Shearer’s lemma, and other related results in the literature are considered. Some of the derived information inequalities are new, and also known results (such as a generalized version of Han’s inequality) are reproduced in a simple and unified way. In its second part, this paper applies the generalized Han’s inequality to analyze a problem in extremal graph theory. This problem is motivated and analyzed from the perspective of information theory, and the analysis leads to generalized and refined bounds. The two parts of this paper are meant to be independently accessible to the reader. Full article

(This article belongs to the Special Issue Information and Divergence Measures)

20 pages, 309 KiB

Open AccessEditor’s ChoiceArticle

Quantum Gravity If Non-Locality Is Fundamental

by Stuart A. Kauffman

Entropy 2022, 24(4), 554; https://doi.org/10.3390/e24040554 - 15 Apr 2022

Cited by 10 | Viewed by 3922

Abstract

I take non-locality to be the Michelson–Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. [...] Read more.

I take non-locality to be the Michelson–Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: (i). if we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. (ii). There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no “emergence” of spacetime. If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: matter not only curves spacetime, but “creates” spacetime. We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity. This quantum creation of spacetime consists of: (i) fully non-local entangled coherent quantum variables. (ii) The onset of locality via decoherence. (iii) A metric in Hilbert space among entangled quantum variables by the sub-additive von Neumann entropy between pairs of variables. (iv) Mapping from metric distances in Hilbert space to metric distances in classical spacetime by episodic actualization events. (v) Discrete spacetime is the relations among these discrete actualization events. (vi) “Now” is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously. (vii) The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. (viii) The arrow of time history of these events is recorded in the very structure of the spacetime constructed. (ix) Actual Time is a succession of two or more actual events. The theory inevitably yields a UV cutoff of a new type. The cutoff is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition. This quantum creation of spacetime modifies General Relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity. Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at “Actual Now” are discussed. Possible observational and experimental tests based on: (i). the existence of Sub- Planckian photons, (ii). knee and ankle discontinuities in the high-energy gamma ray spectrum, and (iii). possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use. The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful. Full article

18 pages, 12693 KiB

Open AccessEditor’s ChoiceArticle

Recasting the (Synchrosqueezed) Short-Time Fourier Transform as an Instantaneous Spectrum

by Steven Sandoval and Phillip L. De Leon

Entropy 2022, 24(4), 518; https://doi.org/10.3390/e24040518 - 6 Apr 2022

Cited by 11 | Viewed by 3212

Abstract

In a previous work, we proposed a time-frequency analysis called instantaneous spectral analysis (ISA), which generalizes the notion of the Fourier spectrum and in which instantaneous frequency is utilized to the fullest extent. In this paper, we recast both the Fourier transform (FT) [...] Read more.

In a previous work, we proposed a time-frequency analysis called instantaneous spectral analysis (ISA), which generalizes the notion of the Fourier spectrum and in which instantaneous frequency is utilized to the fullest extent. In this paper, we recast both the Fourier transform (FT) and filterbank (FB) interpretations of the short-time Fourier transform (STFT) as instantaneous spectra. We show that to recast the FB interpretation of STFT as an instantaneous spectrum with valid structure, frequency reassignment is a fundamental necessity, thus demonstrating that this IS is closely related to the synchrosqueezed STFT. This result provides a new theoretical motivation for the synchrosqueezed STFT. Finally, we illustrate through example the instantaneous spectra corresponding to the FT and FB interpretations of STFT using two closed-form examples. Full article

(This article belongs to the Special Issue Time-Frequency Analysis, AM-FM Models, and Mode Decompositions)

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22 pages, 741 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Quantum Coherences and Classical Inhomogeneities as Equivalent Thermodynamics Resources

by Andrew Smith, Kanupriya Sinha and Christopher Jarzynski

Entropy 2022, 24(4), 474; https://doi.org/10.3390/e24040474 - 29 Mar 2022

Cited by 6 | Viewed by 5646

Abstract

Quantum energy coherences represent a thermodynamic resource, which can be exploited to extract energy from a thermal reservoir and deliver that energy as work. We argue that there exists a closely analogous classical thermodynamic resource, namely, energy-shell inhomogeneities in the phase space distribution [...] Read more.

Quantum energy coherences represent a thermodynamic resource, which can be exploited to extract energy from a thermal reservoir and deliver that energy as work. We argue that there exists a closely analogous classical thermodynamic resource, namely, energy-shell inhomogeneities in the phase space distribution of a system’s initial state. We compare the amount of work that can be obtained from quantum coherences with the amount that can be obtained from classical inhomogeneities, and find them to be equal in the semiclassical limit. We thus conclude that coherences do not provide a unique thermodynamic advantage of quantum systems over classical systems, in situations where a well-defined semiclassical correspondence exists. Full article

(This article belongs to the Special Issue Quantum Darwinism and Friends)

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18 pages, 2679 KiB

Open AccessEditor’s ChoiceArticle

Entropy Generation during Head-On Interaction of Premixed Flames with Inert Walls within Turbulent Boundary Layers

by Sanjeev Kr. Ghai, Umair Ahmed, Nilanjan Chakraborty and Markus Klein

Entropy 2022, 24(4), 463; https://doi.org/10.3390/e24040463 - 27 Mar 2022

Cited by 8 | Viewed by 2413

Abstract

The statistical behaviours of different entropy generation mechanisms in the head-on interaction of turbulent premixed flames with a chemically inert wall within turbulent boundary layers have been analysed using Direct Numerical Simulation data. The entropy generation characteristics in the case of head-on premixed [...] Read more.

The statistical behaviours of different entropy generation mechanisms in the head-on interaction of turbulent premixed flames with a chemically inert wall within turbulent boundary layers have been analysed using Direct Numerical Simulation data. The entropy generation characteristics in the case of head-on premixed flame interaction with an isothermal wall is compared to that for an adiabatic wall. It has been found that entropy generation due to chemical reaction, thermal diffusion and molecular mixing remain comparable when the flame is away from the wall for both wall boundary conditions. However, the wall boundary condition affects the entropy generation during flame-wall interaction. In the case of isothermal wall, the entropy generation due to chemical reaction vanishes because of flame quenching and the entropy generation due to thermal diffusion becomes the leading entropy generator at the wall. By contrast, the entropy generation due to thermal diffusion and molecular mixing decrease at the adiabatic wall because of the vanishing wall-normal components of the gradients of temperature and species mass/mole fractions. These differences have significant effects on the overall entropy generation rate during flame-wall interaction, which suggest that combustor wall cooling needs to be optimized from the point of view of structural integrity and thermodynamic irreversibility. Full article

(This article belongs to the Special Issue Entropy Generation Analysis in Near-Wall Turbulent Flow)

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12 pages, 894 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

A Robust Protocol for Entropy Measurement in Mesoscopic Circuits

by Timothy Child, Owen Sheekey, Silvia Lüscher, Saeed Fallahi, Geoffrey C. Gardner, Michael Manfra and Joshua Folk

Entropy 2022, 24(3), 417; https://doi.org/10.3390/e24030417 - 17 Mar 2022

Cited by 15 | Viewed by 3987

Abstract

Previous measurements utilizing Maxwell relations to measure change in entropy, S, demonstrated remarkable accuracy in measuring the spin-1/2 entropy of electrons in a weakly coupled quantum dot. However, these previous measurements relied upon prior knowledge of the charge transition lineshape. This had [...] Read more.

Previous measurements utilizing Maxwell relations to measure change in entropy, S, demonstrated remarkable accuracy in measuring the spin-1/2 entropy of electrons in a weakly coupled quantum dot. However, these previous measurements relied upon prior knowledge of the charge transition lineshape. This had the benefit of making the quantitative determination of entropy independent of scale factors in the measurement itself but at the cost of limiting the applicability of the approach to simple systems. To measure the entropy of more exotic mesoscopic systems, a more flexible analysis technique may be employed; however, doing so requires a precise calibration of the measurement. Here, we give details on the necessary improvements made to the original experimental approach and highlight some of the common challenges (along with strategies to overcome them) that other groups may face when attempting this type of measurement. Full article

(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)

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14 pages, 3369 KiB

Open AccessEditor’s ChoiceArticle

A Multi-Classification Hybrid Quantum Neural Network Using an All-Qubit Multi-Observable Measurement Strategy

by Yi Zeng, Hao Wang, Jin He, Qijun Huang and Sheng Chang

Entropy 2022, 24(3), 394; https://doi.org/10.3390/e24030394 - 11 Mar 2022

Cited by 31 | Viewed by 8202

Abstract

Quantum machine learning is a promising application of quantum computing for data classification. However, most of the previous research focused on binary classification, and there are few studies on multi-classification. The major challenge comes from the limitations of near-term quantum devices on the [...] Read more.

Quantum machine learning is a promising application of quantum computing for data classification. However, most of the previous research focused on binary classification, and there are few studies on multi-classification. The major challenge comes from the limitations of near-term quantum devices on the number of qubits and the size of quantum circuits. In this paper, we propose a hybrid quantum neural network to implement multi-classification of a real-world dataset. We use an average pooling downsampling strategy to reduce the dimensionality of samples, and we design a ladder-like parameterized quantum circuit to disentangle the input states. Besides this, we adopt an all-qubit multi-observable measurement strategy to capture sufficient hidden information from the quantum system. The experimental results show that our algorithm outperforms the classical neural network and performs especially well on different multi-class datasets, which provides some enlightenment for the application of quantum computing to real-world data on near-term quantum processors. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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16 pages, 1277 KiB

Open AccessEditor’s ChoiceArticle

Information Field Theory and Artificial Intelligence

by Torsten Enßlin

Entropy 2022, 24(3), 374; https://doi.org/10.3390/e24030374 - 7 Mar 2022

Cited by 7 | Viewed by 4358

Abstract

Information field theory (IFT), the information theory for fields, is a mathematical framework for signal reconstruction and non-parametric inverse problems. Artificial intelligence (AI) and machine learning (ML) aim at generating intelligent systems, including such for perception, cognition, and learning. This overlaps with IFT, [...] Read more.

Information field theory (IFT), the information theory for fields, is a mathematical framework for signal reconstruction and non-parametric inverse problems. Artificial intelligence (AI) and machine learning (ML) aim at generating intelligent systems, including such for perception, cognition, and learning. This overlaps with IFT, which is designed to address perception, reasoning, and inference tasks. Here, the relation between concepts and tools in IFT and those in AI and ML research are discussed. In the context of IFT, fields denote physical quantities that change continuously as a function of space (and time) and information theory refers to Bayesian probabilistic logic equipped with the associated entropic information measures. Reconstructing a signal with IFT is a computational problem similar to training a generative neural network (GNN) in ML. In this paper, the process of inference in IFT is reformulated in terms of GNN training. In contrast to classical neural networks, IFT based GNNs can operate without pre-training thanks to incorporating expert knowledge into their architecture. Furthermore, the cross-fertilization of variational inference methods used in IFT and ML are discussed. These discussions suggest that IFT is well suited to address many problems in AI and ML research and application. Full article

(This article belongs to the Special Issue MaxEnt 2020/2021—The 40th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering)

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14 pages, 1209 KiB

Open AccessEditor’s ChoiceArticle

Power-Optimal Control of a Stirling Engine’s Frictional Piston Motion

by Raphael Paul, Abdellah Khodja, Andreas Fischer, Robin Masser and Karl Heinz Hoffmann

Entropy 2022, 24(3), 362; https://doi.org/10.3390/e24030362 - 3 Mar 2022

Cited by 14 | Viewed by 2840

Abstract

The power output of Stirling engines can be optimized by several means. In this study, the focus is on potential performance improvements that can be achieved by optimizing the piston motion of an alpha-Stirling engine in the presence of dissipative processes, in particular [...] Read more.

The power output of Stirling engines can be optimized by several means. In this study, the focus is on potential performance improvements that can be achieved by optimizing the piston motion of an alpha-Stirling engine in the presence of dissipative processes, in particular mechanical friction. We use a low-effort endoreversible Stirling engine model, which allows for the incorporation of finite heat and mass transfer as well as the friction caused by the piston motion. Instead of performing a parameterization of the piston motion and optimizing these parameters, we here use an indirect iterative gradient method that is based on Pontryagin’s maximum principle. For the varying friction coefficient, the optimization results are compared to both, a harmonic piston motion and optimization results found in a previous study, where a parameterized piston motion had been used. Thus we show how much performance can be improved by using the more sophisticated and numerically more expensive iterative gradient method. Full article

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22 pages, 743 KiB

Open AccessEditor’s ChoiceReview

The Free Energy Principle for Perception and Action: A Deep Learning Perspective

by Pietro Mazzaglia, Tim Verbelen, Ozan Çatal and Bart Dhoedt

Entropy 2022, 24(2), 301; https://doi.org/10.3390/e24020301 - 21 Feb 2022

Cited by 63 | Viewed by 10619

Abstract

The free energy principle, and its corollary active inference, constitute a bio-inspired theory that assumes biological agents act to remain in a restricted set of preferred states of the world, i.e., they minimize their free energy. Under this principle, biological agents learn a [...] Read more.

The free energy principle, and its corollary active inference, constitute a bio-inspired theory that assumes biological agents act to remain in a restricted set of preferred states of the world, i.e., they minimize their free energy. Under this principle, biological agents learn a generative model of the world and plan actions in the future that will maintain the agent in an homeostatic state that satisfies its preferences. This framework lends itself to being realized in silico, as it comprehends important aspects that make it computationally affordable, such as variational inference and amortized planning. In this work, we investigate the tool of deep learning to design and realize artificial agents based on active inference, presenting a deep-learning oriented presentation of the free energy principle, surveying works that are relevant in both machine learning and active inference areas, and discussing the design choices that are involved in the implementation process. This manuscript probes newer perspectives for the active inference framework, grounding its theoretical aspects into more pragmatic affairs, offering a practical guide to active inference newcomers and a starting point for deep learning practitioners that would like to investigate implementations of the free energy principle. Full article

(This article belongs to the Special Issue Emerging Methods in Active Inference)

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15 pages, 9833 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Correlations, Information Backflow, and Objectivity in a Class of Pure Dephasing Models

by Nina Megier, Andrea Smirne, Steve Campbell and Bassano Vacchini

Entropy 2022, 24(2), 304; https://doi.org/10.3390/e24020304 - 21 Feb 2022

Cited by 9 | Viewed by 2842

Abstract

We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a dephasing model with different initial conditions, where the state of the initial environment represents a tunable degree of [...] Read more.

We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a dephasing model with different initial conditions, where the state of the initial environment represents a tunable degree of freedom that qualitatively and quantitatively affects the correlation profiles, but nevertheless results in the same reduced dynamics for the system. We apply recently developed tools for the characterisation of non-Markovianity to carefully assess the role that correlations, as quantified by the (quantum) Jensen–Shannon divergence and relative entropy, as well as changes in the environmental state, play in whether the conditions for classical objectivity within the quantum Darwinism paradigm are met. We demonstrate that for precisely the same non-Markovian reduced dynamics of the system arising from different microscopic models, some exhibit quantum Darwinistic features, while others show that no meaningful notion of classical objectivity is present. Furthermore, our results highlight that the non-Markovian nature of an environment does not a priori prevent a system from redundantly proliferating relevant information, but rather it is the system’s ability to establish the requisite correlations that is the crucial factor in the manifestation of classical objectivity. Full article

(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)

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32 pages, 1028 KiB

Open AccessEditor’s ChoiceReview

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

by Michael E. Cates, Étienne Fodor, Tomer Markovich, Cesare Nardini and Elsen Tjhung

Entropy 2022, 24(2), 254; https://doi.org/10.3390/e24020254 - 9 Feb 2022

Cited by 22 | Viewed by 3194

Abstract

Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in [...] Read more.

Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing, for simplicity, on models with a purely diffusive scalar field, such as ‘Model B’ which describes phase separation in binary fluid mixtures. We address the requirement that the steady-state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in a thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for ‘active field theories’ in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR), we must make a careful treatment of so-called ‘spurious drift’ and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative via off-diagonal couplings to additional fields that thermodynamically encode the underlying chemical processes responsible for activity. In this case, the spurious drift terms need careful accounting, not just to evaluate correctly the EPR but also to numerically implement the Langevin dynamics itself. Full article

(This article belongs to the Special Issue Modeling and Simulation of Complex Fluid Flows)

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27 pages, 883 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Coupled Transport Effects in Solid Oxide Fuel Cell Modeling

by Aydan Gedik, Nico Lubos and Stephan Kabelac

Entropy 2022, 24(2), 224; https://doi.org/10.3390/e24020224 - 31 Jan 2022

Cited by 8 | Viewed by 3875

Abstract

With its outstanding performance characteristics, the SOFC represents a promising technology for integration into the current energy supply system. For cell development and optimization, a reliable quantitative description of the transport mechanisms and the resulting losses are relevant. The local transport processes are [...] Read more.

With its outstanding performance characteristics, the SOFC represents a promising technology for integration into the current energy supply system. For cell development and optimization, a reliable quantitative description of the transport mechanisms and the resulting losses are relevant. The local transport processes are calculated by a 1D model based on the non-equilibrium thermodynamics (NET). The focus of this study is the mass transport in the gas diffusion layers (GDL), which was described as simplified by Fick’s law in a previously developed model. This is first replaced by the Dusty-Gas model (DGM) and then by the thermal diffusion (Soret effect) approach. The validation of the model was performed by measuring

U, j

-characteristics resulting in a maximum deviation of experimental to simulated cell voltage to up to 0.93%. It is shown that, under the prevailing temperature, gradients the Soret effect can be neglected, but the extension to the DGM has to be considered. The temperature and heat flow curves illustrate the relevance of the Peltier effects. At

T = 1123.15

K and

j = 8000

A/m², 64.44% of the total losses occur in the electrolyte. The exergetic efficiency for this operating point is 0.42. Since lower entropy production rates can be assumed in the GDL, the primary need is to investigate alternative electrolyte materials. Full article

(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)

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32 pages, 1214 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Nonequilibrium Thermodynamics of Polymeric Liquids via Atomistic Simulation

by Brian Joseph Edwards, Mohammad Hadi Nafar Sefiddashti and Bamin Khomami

Entropy 2022, 24(2), 175; https://doi.org/10.3390/e24020175 - 25 Jan 2022

Cited by 3 | Viewed by 3551

Abstract

The challenge of calculating nonequilibrium entropy in polymeric liquids undergoing flow was addressed from the perspective of extending equilibrium thermodynamics to include internal variables that quantify the internal microstructure of chain-like macromolecules and then applying these principles to nonequilibrium conditions under the presumption [...] Read more.

The challenge of calculating nonequilibrium entropy in polymeric liquids undergoing flow was addressed from the perspective of extending equilibrium thermodynamics to include internal variables that quantify the internal microstructure of chain-like macromolecules and then applying these principles to nonequilibrium conditions under the presumption of an evolution of quasie equilibrium states in which the requisite internal variables relax on different time scales. The nonequilibrium entropy can be determined at various levels of coarse-graining of the polymer chains by statistical expressions involving nonequilibrium distribution functions that depend on the type of flow and the flow strength. Using nonequilibrium molecular dynamics simulations of a linear, monodisperse, entangled C₁₀₀₀H₂₀₀₂ polyethylene melt, nonequilibrium entropy was calculated directly from the nonequilibrium distribution functions, as well as from their second moments, and also using the radial distribution function at various levels of coarse-graining of the constituent macromolecular chains. Surprisingly, all these different methods of calculating the nonequilibrium entropy provide consistent values under both planar Couette and planar elongational flows. Combining the nonequilibrium entropy with the internal energy allows determination of the Helmholtz free energy, which is used as a generating function of flow dynamics in nonequilibrium thermodynamic theory. Full article

(This article belongs to the Special Issue Modeling and Simulation of Complex Fluid Flows)

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30 pages, 1722 KiB

Open AccessEditor’s ChoiceArticle

Unraveling Hidden Major Factors by Breaking Heterogeneity into Homogeneous Parts within Many-System Problems

by Elizabeth P. Chou, Ting-Li Chen and Hsieh Fushing

Entropy 2022, 24(2), 170; https://doi.org/10.3390/e24020170 - 24 Jan 2022

Cited by 6 | Viewed by 2462

Abstract

For a large ensemble of complex systems, a Many-System Problem (MSP) studies how heterogeneity constrains and hides structural mechanisms, and how to uncover and reveal hidden major factors from homogeneous parts. All member systems in an MSP share common governing principles of dynamics, [...] Read more.

For a large ensemble of complex systems, a Many-System Problem (MSP) studies how heterogeneity constrains and hides structural mechanisms, and how to uncover and reveal hidden major factors from homogeneous parts. All member systems in an MSP share common governing principles of dynamics, but differ in idiosyncratic characteristics. A typical dynamic is found underlying response features with respect to covariate features of quantitative or qualitative data types. Neither all-system-as-one-whole nor individual system-specific functional structures are assumed in such response-vs-covariate (Re–Co) dynamics. We developed a computational protocol for identifying various collections of major factors of various orders underlying Re–Co dynamics. We first demonstrate the immanent effects of heterogeneity among member systems, which constrain compositions of major factors and even hide essential ones. Secondly, we show that fuller collections of major factors are discovered by breaking heterogeneity into many homogeneous parts. This process further realizes Anderson’s “More is Different” phenomenon. We employ the categorical nature of all features and develop a Categorical Exploratory Data Analysis (CEDA)-based major factor selection protocol. Information theoretical measurements—conditional mutual information and entropy—are heavily used in two selection criteria: C1—confirmable and C2—irreplaceable. All conditional entropies are evaluated through contingency tables with algorithmically computed reliability against the finite sample phenomenon. We study one artificially designed MSP and then two real collectives of Major League Baseball (MLB) pitching dynamics with 62 slider pitchers and 199 fastball pitchers, respectively. Finally, our MSP data analyzing techniques are applied to resolve a scientific issue related to the Rosenberg Self-Esteem Scale. Full article

(This article belongs to the Special Issue Information Complexity in Structured Data)

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25 pages, 5419 KiB

Open AccessEditor’s ChoiceArticle

Applying Hybrid ARIMA-SGARCH in Algorithmic Investment Strategies on S&P500 Index

by Nguyen Vo and Robert Ślepaczuk

Entropy 2022, 24(2), 158; https://doi.org/10.3390/e24020158 - 20 Jan 2022

Cited by 27 | Viewed by 7196

Abstract

This research aims to compare the performance of ARIMA as a linear model with that of the combination of ARIMA and GARCH family models to forecast S&P500 log returns in order to construct algorithmic investment strategies on this index. We used the data [...] Read more.

This research aims to compare the performance of ARIMA as a linear model with that of the combination of ARIMA and GARCH family models to forecast S&P500 log returns in order to construct algorithmic investment strategies on this index. We used the data collected from Yahoo Finance with daily frequency for the period from 1 January 2000 to 31 December 2019. By using a rolling window approach, we compared ARIMA with the hybrid models to examine whether hybrid ARIMA-SGARCH and ARIMA-EGARCH can really reflect the specific time-series characteristics and have better predictive power than the simple ARIMA model. In order to assess the precision and quality of these models in forecasting, we compared their equity lines, their forecasting error metrics (MAE, MAPE, RMSE, MAPE), and their performance metrics (annualized return compounded, annualized standard deviation, maximum drawdown, information ratio, and adjusted information ratio). The main contribution of this research is to show that the hybrid models outperform ARIMA and the benchmark (Buy&Hold strategy on S&P500 index) over the long term. These results are not sensitive to varying window sizes, the type of distribution, and the type of the GARCH model. Full article

(This article belongs to the Special Issue Methods in Artificial Intelligence and Information Processing)

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14 pages, 821 KiB

Open AccessEditor’s ChoiceArticle

Role of Time Scales in the Coupled Epidemic-Opinion Dynamics on Multiplex Networks

by Robert Jankowski and Anna Chmiel

Entropy 2022, 24(1), 105; https://doi.org/10.3390/e24010105 - 9 Jan 2022

Cited by 8 | Viewed by 2954

Abstract

Modelling the epidemic’s spread on multiplex networks, considering complex human behaviours, has recently gained the attention of many scientists. In this work, we study the interplay between epidemic spreading and opinion dynamics on multiplex networks. An agent in the epidemic layer could remain [...] Read more.

Modelling the epidemic’s spread on multiplex networks, considering complex human behaviours, has recently gained the attention of many scientists. In this work, we study the interplay between epidemic spreading and opinion dynamics on multiplex networks. An agent in the epidemic layer could remain in one of five distinct states, resulting in the SIRQD model. The agent’s attitude towards respecting the restrictions of the pandemic plays a crucial role in its prevalence. In our model, the agent’s point of view could be altered by either conformism mechanism, social pressure, or independent actions. As the underlying opinion model, we leverage the q-voter model. The entire system constitutes a coupled opinion–dynamic model where two distinct processes occur. The question arises of how to properly align these dynamics, i.e., whether they should possess equal or disparate timescales. This paper highlights the impact of different timescales of opinion dynamics on epidemic spreading, focusing on the time and the infection’s peak. Full article

(This article belongs to the Special Issue Entropy and Social Physics)

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21 pages, 2718 KiB

Open AccessEditor’s ChoiceArticle

Thermodynamic Rarity Assessment of Mobile Phone PCBs: A Physical Criticality Indicator in Times of Shortage

by Jorge Torrubia, Antonio Valero and Alicia Valero

Entropy 2022, 24(1), 100; https://doi.org/10.3390/e24010100 - 8 Jan 2022

Cited by 5 | Viewed by 2182

Abstract

Rising prices in energy, raw materials, and shortages of critical raw materials (CRMs) for renewable energies or electric vehicles are jeopardizing the transition to a low-carbon economy. Therefore, managing scarce resources must be a priority for governments. To that end, appropriate indicators that [...] Read more.

Rising prices in energy, raw materials, and shortages of critical raw materials (CRMs) for renewable energies or electric vehicles are jeopardizing the transition to a low-carbon economy. Therefore, managing scarce resources must be a priority for governments. To that end, appropriate indicators that can identify the criticality of raw materials and products is key. Thermodynamic rarity (TR) is an exergy-based indicator that measures the scarcity of elements in the earth’s crust and the energy intensity to extract and refine them. This paper uses TR to study 70 Mobile Phone (MP) Printed Circuit Boards (PCBs) samples. Results show that an average MP PCB has a TR of 88 MJ per unit, indicating their intensive use of valuable materials. Every year the embedded TR increases by 36,250 GWh worldwide -similar to the electricity consumed by Denmark in 2019- due to annual production of MP. Pd, Ta and Au embedded in MP PCBs worldwide between 2007 and 2021 contribute to 90% of the overall TR, which account for 75, 600 and 250 tones, respectively, and increasing by 11% annually. This, coupled with the short lifespan of MP, makes PCBs an important potential source of secondary resources. Full article

(This article belongs to the Section Thermodynamics)

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10 pages, 344 KiB

Open AccessEditor’s ChoiceArticle

Permutation Entropy of Weakly Noise-Affected Signals

by Leonardo Ricci and Antonio Politi

Entropy 2022, 24(1), 54; https://doi.org/10.3390/e24010054 - 28 Dec 2021

Cited by 5 | Viewed by 2326

Abstract

We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed [...] Read more.

We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed light on the scenario, we perform a multifractal analysis, which allows highlighting the emergence of many poorly populated symbolic sequences generated by the stochastic fluctuations. We finally make use of this information to reconstruct the noiseless permutation entropy. While this approach works quite well for Hénon and tent maps, it is much less effective in the case of hyperchaos. We argue about the underlying motivations. Full article

(This article belongs to the Special Issue Ordinal and Pattern-Based Quantifiers for Complex Time Series Analysis)

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18 pages, 323 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media

by Dick Bedeaux and Signe Kjelstrup

Entropy 2022, 24(1), 46; https://doi.org/10.3390/e24010046 - 27 Dec 2021

Cited by 15 | Viewed by 3441

Abstract

A thermodynamic description of porous media must handle the size- and shape-dependence of media properties, in particular on the nano-scale. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average [...] Read more.

A thermodynamic description of porous media must handle the size- and shape-dependence of media properties, in particular on the nano-scale. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average densities suitable for integration on the course-grained scale, by applying Hill’s thermodynamics of small systems to the subsystems of the medium. We argue that the average densities of the porous medium, when defined in a proper way, obey the Gibbs equation. All contributions are additive or weakly coupled. From the Gibbs equation and the balance equations, we then derive the entropy production in the standard way, for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in boundary pressures, temperatures, and chemical potentials. Linear relations between thermodynamic fluxes and forces follow for the control volume. Fluctuation-dissipation theorems are formulated for the first time, for the fluctuating contributions to fluxes in the porous medium. These give an added possibility for determination of the Onsager conductivity matrix for transport through porous media. Practical possibilities are discussed. Full article

(This article belongs to the Special Issue Modeling and Simulation of Complex Fluid Flows)

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15 pages, 1233 KiB

Open AccessEditor’s ChoiceArticle

Common Environmental Effects on Quantum Thermal Transistor

by Yu-Qiang Liu, Deng-Hui Yu and Chang-Shui Yu

Entropy 2022, 24(1), 32; https://doi.org/10.3390/e24010032 - 24 Dec 2021

Cited by 19 | Viewed by 3280

Abstract

Quantum thermal transistor is a microscopic thermodynamical device that can modulate and amplify heat current through two terminals by the weak heat current at the third terminal. Here we study the common environmental effects on a quantum thermal transistor made up of three [...] Read more.

Quantum thermal transistor is a microscopic thermodynamical device that can modulate and amplify heat current through two terminals by the weak heat current at the third terminal. Here we study the common environmental effects on a quantum thermal transistor made up of three strong-coupling qubits. It is shown that the functions of the thermal transistor can be maintained and the amplification rate can be modestly enhanced by the skillfully designed common environments. In particular, the presence of a dark state in the case of the completely correlated transitions can provide an additional external channel to control the heat currents without any disturbance of the amplification rate. These results show that common environmental effects can offer new insights into improving the performance of quantum thermal devices. Full article

(This article belongs to the Section Quantum Information)

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18 pages, 5484 KiB

Open AccessEditor’s ChoiceArticle

Alternate Entropy Computations by Applying Recurrence Matrix Masking

by Charles L. Webber, Jr.

Entropy 2022, 24(1), 16; https://doi.org/10.3390/e24010016 - 23 Dec 2021

Cited by 4 | Viewed by 3672

Abstract

In practicality, recurrence analyses of dynamical systems can only process short sections of signals that may be infinitely long. By necessity, the recurrence plot and its quantifications are constrained within a truncated triangle that clips the signals at its borders. Recurrence variables defined [...] Read more.

In practicality, recurrence analyses of dynamical systems can only process short sections of signals that may be infinitely long. By necessity, the recurrence plot and its quantifications are constrained within a truncated triangle that clips the signals at its borders. Recurrence variables defined within these confining borders can be influenced more or less by truncation effects depending upon the system under evaluation. In this study, the question being asked is what if the boundary borders were tilted, what would be the effect on all recurrence variables? This question was prompted by the observation that line entropy values are maximized for highly periodic systems in which the infinitely long line elements are truncated to different unique lengths. However, by redefining the recurrence plot area to a 45-degree tilted box within the triangular area, the diagonal lines would consequently be truncated to identical lengths. Such masking would minimize the line entropy to 0.000 bits/bin. However, what new truncation influences would be imposed on the other recurrence variables? This question is examined by comparing recurrence variables computed with the triangular recurrence area versus boxed recurrence area. Examples include the logistic equation (mathematical series), the Dow Jones Industrial Average over a decade (real-word data), and a square wave pulse (toy series). Good agreement among the variables in terms of timing and amplitude was found for most, but not all variables. These important results are discussed. Full article

(This article belongs to the Special Issue Complexity Science in Human Change: Research, Models, Clinical Applications)

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14 pages, 1409 KiB

Open AccessEditor’s ChoiceArticle

MFF-Net: Deepfake Detection Network Based on Multi-Feature Fusion

by Lei Zhao, Mingcheng Zhang, Hongwei Ding and Xiaohui Cui

Entropy 2021, 23(12), 1692; https://doi.org/10.3390/e23121692 - 17 Dec 2021

Cited by 24 | Viewed by 5571

Abstract

Significant progress has been made in generating counterfeit images and videos. Forged videos generated by deepfaking have been widely spread and have caused severe societal impacts, which stir up public concern about automatic deepfake detection technology. Recently, many deepfake detection methods based on [...] Read more.

Significant progress has been made in generating counterfeit images and videos. Forged videos generated by deepfaking have been widely spread and have caused severe societal impacts, which stir up public concern about automatic deepfake detection technology. Recently, many deepfake detection methods based on forged features have been proposed. Among the popular forged features, textural features are widely used. However, most of the current texture-based detection methods extract textures directly from RGB images, ignoring the mature spectral analysis methods. Therefore, this research proposes a deepfake detection network fusing RGB features and textural information extracted by neural networks and signal processing methods, namely, MFF-Net. Specifically, it consists of four key components: (1) a feature extraction module to further extract textural and frequency information using the Gabor convolution and residual attention blocks; (2) a texture enhancement module to zoom into the subtle textural features in shallow layers; (3) an attention module to force the classifier to focus on the forged part; (4) two instances of feature fusion to firstly fuse textural features from the shallow RGB branch and feature extraction module and then to fuse the textural features and semantic information. Moreover, we further introduce a new diversity loss to force the feature extraction module to learn features of different scales and directions. The experimental results show that MFF-Net has excellent generalization and has achieved state-of-the-art performance on various deepfake datasets. Full article

(This article belongs to the Topic Machine and Deep Learning)

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