Notion Of Entropy Research Articles

Invariance Properties of Controlled Stochastic Nonlinear Systems Under Information Constraints

Given a stochastic nonlinear system controlled over a possibly noisy communication channel, the article studies the largest class of channels for which there exist coding and control policies so that the closed-loop system is stochastically stable. The stability criterion considered is asymptotic mean stationarity (AMS). In this article, we develop a general method based on ergodic theory and probability to derive fundamental bounds on information transmission requirements leading to stabilization. Through this method, we develop a new notion of entropy which is tailored to derive lower bounds for AMS for both noise-free and noisy channels. The bounds obtained through probabilistic and ergodic-theoretic analysis are more refined in comparison with the bounds obtained earlier via information-theoretic methods. Moreover, our approach is more versatile in view of the models considered and allows for finer lower bounds when the AMS measure is known to admit further properties, such as moment bounds.

A notion of entropy for causal fermion systems

A notion of entropy is introduced for causal fermion systems. This entropy is a measure of the state of disorder of a causal fermion system at a given time compared to the vacuum. The definition is given both in the finite and infinite-dimensional settings. General properties of the entropy are analyzed.

Thermodynamics of Reduced State of the Field.

Recent years have seen the flourishing of research devoted to quantum effects on mesoscopic and macroscopic scales. In this context, in Entropy 2019, 21, 705, a formalism aiming at describing macroscopic quantum fields, dubbed Reduced State of the Field (RSF), was envisaged. While, in the original work, a proper notion of entropy for macroscopic fields, together with their dynamical equations, was derived, here, we expand thermodynamic analysis of the RSF, discussing the notion of heat, solving dynamical equations in various regimes of interest, and showing the thermodynamic implications of these solutions.

Estimating the Entropy and Residual Entropy of a Lomax Distribution under Generalized Type-II Hybrid Censoring

The Lomax distribution (or Pareto II) was first introduced by K. S. Lomax in 1954. It can be readily applied to a wide range of situations including applications in the analysis of the business failure life time data, economics, and actuarial science, income and wealth inequality, size of cities, engineering, lifetime, and reliability modeling. In his pioneering paper, Shannon 1948 defined the notion of entropy as a mathematical measure of information, which is sometimes called Shannon entropy in his honor. He laid the groundwork for a new branch of mathematics in which the notion of entropy plays a fundamental role over different areas of applications such as statistics, information theory, financial analysis, and data compression. [Ebrahimi and Pellerey 14] introduced the residual entropy function because the entropy shouldn't be applied to a system that has survived for some units of time, and therefore, the residual entropy is used to measure the ageing and characterize, classify and order lifetime distributions. In this paper, the estimation of the entropy and residual entropy of a two parameter Lomax distribution under a generalized Type-II hybrid censoring scheme are introduced. The maximum likelihood estimation for the entropy is provided and the Bayes estimation for the residual entropy is obtained. Simulation studies to assess the performance of the estimates with different sample sizes are described, finally conclusions are discussed.

How many laws has thermodynamics? What is the sense of the entropy notion? Implications for molecular physical chemistry

How many laws has thermodynamics? What is the sense of the entropy notion? Implications for molecular physical chemistry

Beyond the death drive: Entropy and free energy

ABSTRACT In this paper I offer an overview of the possible links between psychoanalytical metapsychology and contemporary work in neuroscience concerning entropy and the free energy principle. After briefly describing the theory of living systems put forward by the neuroscientist Karl Friston based on the notion of entropy, we sum up the use of the notion of free energy by Friston and Freud. I then analyze how these notions improve the intelligibility of psychic functioning and can be associated with several psychoanalytical concepts, in particular the death drive. I approach from the same perspective the regulation of free energy associated with psychic envelopes and early intersubjectivity. It thus appears that the psychic apparatus can be considered at its different levels, from the most primary to the most secondary, as having the essential function of reducing entropy and free energy. Various forms of “failure” of this process of linking, regulation and transformation of energy within the psychic apparatus could be considered as the origin of different psychopathological manifestations as suggested in the last part of this paper.

The Carnot Cycle, Reversibility and Entropy.

The Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still corresponds to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea, current at the time, that heat is motion. It is shown how this view of heat led Clausius to develop the entropy of a body based on the work that could be performed in a reversible process rather than the work that is actually performed in an irreversible process. In consequence, Clausius built into entropy a conflict with energy conservation, which is concerned with actual changes in energy. In this paper, reversibility and irreversibility are investigated by means of a macroscopic formulation of internal mechanisms of damping based on rate equations for the distribution of energy within a gas. It is shown that work processes involving a step change in external pressure, however small, are intrinsically irreversible. However, under idealised conditions of zero damping the gas inside a piston expands and traces out a trajectory through the space of equilibrium states. Therefore, the entropy change due to heat flow from the reservoir matches the entropy change of the equilibrium states. This trajectory can be traced out in reverse as the piston reverses direction, but if the external conditions are adjusted appropriately, the gas can be made to trace out a Carnot cycle in P-V space. The cycle is dynamic as opposed to quasi-static as the piston has kinetic energy equal in difference to the work performed internally and externally.

A Machine Learning-Based Prediction Model for Preterm Birth in Rural India.

Preterm birth (PTB) in a pregnant woman is the most serious issue in the field of Gynaecology and Obstetrics, especially in rural India. In recent years, various clinical prediction models for PTB have been developed to improve the accuracy of learning models. However, to the best of the authors' knowledge, most of them suffer from selecting the most accurate features from the medical dataset in linear time. The present paper attempts to design a machine learning model named as risk prediction conceptual model (RPCM) for the prediction of PTB. In this paper, a feature selection approach is proposed based on the notion of entropy. The novel approach is used to find the best maternal features (responsible for PTB) from the obstetrical dataset and aims to predict the classifier's accuracy at the highest level. The paper first deals with the review of PTB cases (which is neglected in many developing countries including India). Next, we collect obstetrical data from the Community Health Centre of rural areas (Kamdara, Jharkhand). The suggested approach is then applied on collected data to identify the excellent maternal features (text-based symptoms) present in pregnant women in order to classify all birth cases into term birth and PTB. The machine learning part of the model is implemented using three different classifiers, namely, decision tree (DT), logistic regression (LR), and support vector machine (SVM) for PTB prediction. The performance of the classifiers is measured in terms of accuracy, specificity, and sensitivity. Finally, the SVM classifier generates an accuracy of 90.9%, which is higher than other learning classifiers used in this study.

Identifying Influential Nodes in Complex Networks Based on Neighborhood Entropy Centrality

AbstractIdentifying influential nodes is a fundamental and open issue in analysis of the complex networks. The measurement of the spreading capabilities of nodes is an attractive challenge in this field. Node centrality is one of the most popular methods used to identify the influential nodes, which includes the degree centrality (DC), betweenness centrality (BC) and closeness centrality (CC). The DC is an efficient method but not effective. The BC and CC are effective but not efficient. They have high computational complexity. To balance the effectiveness and efficiency, this paper proposes the neighborhood entropy centrality to rank the influential nodes. The proposed method uses the notion of entropy to improve the DC. For evaluating the performance, the susceptible-infected-recovered model is used to simulate the information spreading process of messages on nine real-world networks. The experimental results reveal the accuracy and efficiency of the proposed method.

Metric Versus Topological Receptive Entropy of Semigroup Actions

We study the receptive metric entropy for semigroup actions on probability spaces, inspired by a similar notion of topological entropy introduced by Hofmann and Stoyanov (Adv Math 115:54–98, 1995). We analyze its basic properties and its relation with the classical metric entropy. In the case of semigroup actions on compact metric spaces we compare the receptive metric entropy with the receptive topological entropy looking for a Variational Principle. With this aim we propose several characterizations of the receptive topological entropy. Finally we introduce a receptive local metric entropy inspired by a notion by Bowen generalized in the classical setting of amenable group actions by Zheng and Chen, and we prove partial versions of the Brin–Katok Formula and the local Variational Principle.

Colding Minicozzi entropy in hyperbolic space

This note introduces a notion of entropy for submanifolds of hyperbolic space analogous to the one introduced by Colding and Minicozzi for submanifolds of Euclidean space. Several properties are proved for this quantity including monotonicity along mean curvature flow in low dimensions and a connection with the conformal volume.

An intuitionistic fuzzy entropy approach for supplier selection

Due to apparent flexibility of Intuitionistic Fuzzy Set (IFS) concepts in dealing with the imprecision or uncertainty, these are proving to be quite useful in many application areas for a more human consistent reasoning under imperfectly defined facts and imprecise knowledge. In this paper, we apply notions of entropy and intuitionistic fuzzy sets to present a new fuzzy decision-making approach called intuitionistic fuzzy entropy measure for selection and ranking the suppliers with respect to the attributes. An entropy-based model is formulated and applied to a real case study aiming to examine the rankings of suppliers. Furthermore, the weights for each alternative, with respect to the criteria, are calculated using intuitionistic fuzzy entropy measure. The supplier with the highest weight is selected as the best alternative. This proposed model helps the decision-makers in better understanding of the weight of each criterion without relying on the mere expertise.

Entropy in Thermodynamics: from Foliation to Categorization

AbstractWe overview the notion of entropy in thermodynamics. We start from the smooth case using differential forms on the manifold, which is the natural language for thermodynamics. Then the axiomatic definition of entropy as ordering on a set that is induced by adiabatic processes will be outlined. Finally, the viewpoint of category theory is provided, which reinterprets the ordering structure as a category of pre-ordered sets.

Cosmological constant, information and gedanken experiments with black hole horizons

The cosmological constant if considered as a fundamental constant, provides an information treatment for gravitation problems, both cosmological and of black holes. The efficiency of that approach is shown via gedanken experiments for the information behavior of the horizons for Schwarzschild-de Sitter and Kerr-de Sitter metrics. A notion of entropy regarding any observer and in all possible non-extreme black hole solutions is suggested, linked also to Bekenstein bound. The suggested information approach forbids the existence of naked singularities.

Observations of Hawking radiation: the Page curve and baby universes

We reformulate recent insights into black hole information in a manner emphasizing operationally-defined notions of entropy, Lorentz-signature descriptions, and asymptotically flat spacetimes. With the help of replica wormholes, we find that experiments of asymptotic observers are consistent with black holes as unitary quantum systems, with density of states given by the Bekenstein-Hawking formula. However, this comes at the cost of superselection sectors associated with the state of baby universes. Spacetimes studied by Polchinski and Strominger in 1994 provide a simple illustration of the associated concepts and techniques, and we argue them to be a natural late-time extrapolation of replica wormholes. The work aims to be self-contained and, in particular, to be accessible to readers who have not yet mastered earlier formulations of the ideas above.

Order-Stability in Complex Biological, Social, and AI-Systems from Quantum Information Theory.

This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger’s analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem S composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, We study the following problem: whether the compound system S can maintain “global order” in the situation of an increase of local disorder and if S can preserve the low entropy while other increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of S cannot be less than the entropy of its subsystem . And if a subsystems’s entropy increases, then a system’s entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems’ states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system S (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems—respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in social science and artificial intelligence.

Finite-size corrections in critical symmetry-resolved entanglement

In the presence of a conserved quantity, symmetry-resolved entanglement entropies are a refinement of the usual notion of entanglement entropy of a subsystem. For critical 1d quantum systems, it was recently shown in various contexts that these quantities generally obey entropy equipartition in the scaling limit, i.e. they become independent of the symmetry sector. In this paper, we examine the finite-size corrections to the entropy equipartition phenomenon, and show that the nature of the symmetry group plays a crucial role. In the case of a discrete symmetry group, the corrections decay algebraically with system size, with exponents related to the operators' scaling dimensions. In contrast, in the case of a U(1) symmetry group, the corrections only decay logarithmically with system size, with model-dependent prefactors. We show that the determination of these prefactors boils down to the computation of twisted overlaps.

Does Winning or Losing Change Players’ Engagement in Competitive Games? Experiments in Virtual Reality

Engagement is a key element in game design, and competition is frequently used to enhance players' engagement. However, it is presently unclear how winning or losing might influence players' engagement. We hypothesized that users in a competitive game will increase their level of engagement when they are losing. To test this hypothesis, we created a game in virtual reality in which each user competed against a virtual opponent that was programmed to either underperform, tie with, or overperform the user. We conducted a series of experiments on 72 volunteers who played four rounds of the game, with three rounds against each of the potential virtual opponents and one round alone. We found that user engagement increased when the virtual opponent outperformed the user, compared to when they played alone. A similar increase in user engagement was not registered when the user played against an underperforming or equally performing virtual opponent. To further elucidate the effect of the virtual opponent on user engagement, we applied the information-theoretic notion of transfer entropy, which offers a model-free approach for the inference of causal relationships between dynamical systems. Our findings provide insight into technology-mediated competition and its impact on engagement, thereby opening the door for targeted system interventions to modulate human response.

The Impact of the SARS-CoV-2 Epidemic on World Indices: The Entropy Approach

The coronavirus disease (COVID-19) outbreak started in December 2019 in Wuhan. The virus has spread around the whole world, and it has caused a strong and serious pandemic. Symptoms such as cough, respiratory distress, diarrhea, and fatigue associated with COVID-19 are typical clinical findings. Coronavirus infection has become an important public health concern because of its increasing prevalence, serious complications, and mortality. In light of this information, we examine different entropy methods for world indices (ISE 30, FTSE 100, NIKKEI 225, SP 500, and DAX 30) in the pre-COVID-19 period (02.01.2019–17.11.2019) and the post-COVID-19 period (18.11.2019–23.11.2020) in this article. Besides, we discuss the performances of entropies such as Shannon, Renyi, Tsallis, and approximate entropy (ApEn) in detail and perform the notion of entropy for volatility measure. As a result, we present the numerical results for the data set.

Decimation and interleaving operations in one-sided symbolic dynamics

This paper studies subsets of one-sided shift spaces on a finite alphabet. Such subsets arise in symbolic dynamics, in fractal constructions, and in number theory. We study a family of decimation operations, which extract subsequences of symbol sequences in infinite arithmetic progressions, and show these operations are closed under composition. We also study a family of n-ary interleaving operations, one for each n≥1. Given subsets X0,X1,...,Xn−1 of such a shift space, the n-ary interleaving operation produces a set whose elements combine individual elements xi, one from each Xi, by interleaving their symbol sequences in arithmetic progressions (modn). We determine algebraic relations between decimation and interleaving operations and the shift map. We study set-theoretic n-fold closure operations X↦X[n], which interleave decimations of X of modulus level n. A set is n-factorizable if X=X[n]. The n-fold interleaving operations are closed under composition and are idempotent. To each X we assign the set N(X) of all values n≥1 for which X=X[n]. We characterize the possible sets N(X) as nonempty sets of positive integers that form a distributive lattice under the divisibility partial order and are downward closed under divisibility. We show that all sets of this type occur. We introduce a class of weakly shift-stable sets and show that this class is closed under all decimation, interleaving, and shift operations. We study two notions of entropy for subsets of the full one-sided shift and show that they coincide for weakly shift-stable X, but can be different in general. We give a formula for entropy of interleavings of weakly shift-stable sets in terms of individual entropies.