939 resultados para Topological entropy


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Recently, a group of researchers proposed the concept of entransy by analogy with the electrical energy stored in a capacitor, the entransy being a measure of the ability of a body or a system to transfer heat. In comparative terms, the entransy dissipation rate is related with the loss of heat transfer ability just like the exergy destruction rate is proportional to the loss of work ability, being these losses caused by the irreversibilities related to the thermodynamic processes. Some authors have questioned the need for the concept of entransy, claiming that this concept is only an extension of a well established theory of heat transfer. The objective of this work is show the equivalence between the application of the concepts of entransy and entropy generation rate, which can be verified using various application examples. The application examples used here are the thermodynamic modeling of three physical models of solar energy collectors and a physical model of a sensible heat storage system. Analytical results are shown and compared. The results showed that the application of the concept of entransy provided identical expressions obtained by the concept of entropy generation, indicating a duplication of concepts. (C) 2014 Elsevier Ltd. All rights reserved.

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The technologies are rapidly developing, but some of them present in the computers, as for instance their processing capacity, are reaching their physical limits. It is up to quantum computation offer solutions to these limitations and issues that may arise. In the field of information security, encryption is of paramount importance, being then the development of quantum methods instead of the classics, given the computational power offered by quantum computing. In the quantum world, the physical states are interrelated, thus occurring phenomenon called entanglement. This study presents both a theoretical essay on the merits of quantum mechanics, computing, information, cryptography and quantum entropy, and some simulations, implementing in C language the effects of entropy of entanglement of photons in a data transmission, using Von Neumann entropy and Tsallis entropy.

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We present a systematic investigation of the nature and strength of the hydrogen bonding in HX···HX and CH3X…HX (X = Br, Cl and F) dimers using ab initio MP2/aug-cc-pVTZ calculations in the framework of the quantum theory of atoms in molecules (QTAIM) and electron localisation functions (ELFs) methods. The electron density of the complexes has been characterised, and the hydrogen bonding energy, as well as the QTAIM and ELF parameters, is consistent, providing deep insight into the origin of the hydrogen bonding in these complexes. It was found that in both linear and angular HX…HX and CH3X…HX dimers, F atoms form stronger HB than Br and Cl, but they need short (∼2 Å) X…HX contacts.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e. g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a "fingerprint". Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the "uncertainty" of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them to (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed.

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We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767672]

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Complexity in time series is an intriguing feature of living dynamical systems, with potential use for identification of system state. Although various methods have been proposed for measuring physiologic complexity, uncorrelated time series are often assigned high values of complexity, errouneously classifying them as a complex physiological signals. Here, we propose and discuss a method for complex system analysis based on generalized statistical formalism and surrogate time series. Sample entropy (SampEn) was rewritten inspired in Tsallis generalized entropy, as function of q parameter (qSampEn). qSDiff curves were calculated, which consist of differences between original and surrogate series qSampEn. We evaluated qSDiff for 125 real heart rate variability (HRV) dynamics, divided into groups of 70 healthy, 44 congestive heart failure (CHF), and 11 atrial fibrillation (AF) subjects, and for simulated series of stochastic and chaotic process. The evaluations showed that, for nonperiodic signals, qSDiff curves have a maximum point (qSDiff(max)) for q not equal 1. Values of q where the maximum point occurs and where qSDiff is zero were also evaluated. Only qSDiff(max) values were capable of distinguish HRV groups (p-values 5.10 x 10(-3); 1.11 x 10(-7), and 5.50 x 10(-7) for healthy vs. CHF, healthy vs. AF, and CHF vs. AF, respectively), consistently with the concept of physiologic complexity, and suggests a potential use for chaotic system analysis. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4758815]

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We present a stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation. From the microscopic Schnakenberg expression we get the macroscopic bilinear form for the entropy production rate in terms of fluxes and forces. This is performed by placing the system in contact with two reservoirs with distinct sets of thermodynamic fields and by assuming an appropriate form for the transition rate. The approach is applied to an interacting lattice gas model in contact with two heat and particle reservoirs. On a square lattice, a continuous symmetry breaking phase transition takes place such that at the nonequilibrium ordered phase a heat flow sets in even when the temperatures of the reservoirs are the same. The entropy production rate is found to have a singularity at the critical point of the linear-logarithm type.

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Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement alpha-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry such as the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well as models with discrete symmetries such as the Ising, the Blume-Capel, and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, which depend on the value of a, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the alpha-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the alpha-Renyi entropies is p(alpha) = 2X(epsilon)/alpha for alpha > 1 and p(1) = nu, where X-epsilon denotes the dimensions of the energy operator of the model and nu = 2 for all the models.

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The nonequilibrium stationary state of an irreversible spherical model is investigated on hypercubic lattices. The model is defined by Langevin equations similar to the reversible case, but with asymmetric transition rates. In spite of being irreversible, we have succeeded in finding an explicit form for the stationary probability distribution, which turns out to be of the Boltzmann-Gibbs type. This enables one to evaluate the exact form of the entropy production rate at the stationary state, which is non-zero if the dynamical rules of the transition rates are asymmetric.

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Financial markets can be viewed as a highly complex evolving system that is very sensitive to economic instabilities. The complex organization of the market can be represented in a suitable fashion in terms of complex networks, which can be constructed from stock prices such that each pair of stocks is connected by a weighted edge that encodes the distance between them. In this work, we propose an approach to analyze the topological and dynamic evolution of financial networks based on the stock correlation matrices. An entropy-related measurement is adopted to quantify the robustness of the evolving financial market organization. It is verified that the network topological organization suffers strong variation during financial instabilities and the networks in such periods become less robust. A statistical robust regression model is proposed to quantity the relationship between the network structure and resilience. The obtained coefficients of such model indicate that the average shortest path length is the measurement most related to network resilience coefficient. This result indicates that a collective behavior is observed between stocks during financial crisis. More specifically, stocks tend to synchronize their price evolution, leading to a high correlation between pair of stock prices, which contributes to the increase in distance between them and, consequently, decrease the network resilience. (C) 2012 American Institute of Physics. [doi:10.1063/1.3683467]

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Increasing age is associated with a reduction in overall heart rate variability as well as changes in complexity of physiologic dynamics. The aim of this study was to verify if the alterations in autonomic modulation of heart rate caused by the aging process could be detected by Shannon entropy (SE), conditional entropy (CE) and symbolic analysis (SA). Complexity analysis was carried out in 44 healthy subjects divided into two groups: old (n = 23, 63 +/- A 3 years) and young group (n = 21, 23 +/- A 2). It was analyzed SE, CE [complexity index (CI) and normalized CI (NCI)] and SA (0V, 1V, 2LV and 2ULV patterns) during short heart period series (200 cardiac beats) derived from ECG recordings during 15 min of rest in a supine position. The sequences characterized by three heart periods with no significant variations (0V), and that with two significant unlike variations (2ULV) reflect changes in sympathetic and vagal modulation, respectively. The unpaired t test (or Mann-Whitney rank sum test when appropriate) was used in the statistical analysis. In the aging process, the distributions of patterns (SE) remain similar to young subjects. However, the regularity is significantly different; the patterns are more repetitive in the old group (a decrease of CI and NCI). The amounts of pattern types are different: 0V is increased and 2LV and 2ULV are reduced in the old group. These differences indicate marked change of autonomic regulation. The CE and SA are feasible techniques to detect alteration in autonomic control of heart rate in the old group.

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We used the statistical measurements of information entropy, disequilibrium and complexity to infer a hierarchy of equations of state for two types of compact stars from the broad class of neutron stars, namely, with hadronic composition and with strange quark composition. Our results show that, since order costs energy. Nature would favor the exotic strange stars even though the question of how to form the strange stars cannot be answered within this approach. (C) 2012 Elsevier B.V. All rights reserved.