Entropy In Dynamic Systems

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Entropy in Dynamic Systems

Author : Jan Awrejcewicz
Publisher : MDPI
ISBN 13 : 3039216163
Total Pages : 172 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Entropy in Dynamic Systems by : Jan Awrejcewicz

Download or read book Entropy in Dynamic Systems written by Jan Awrejcewicz and published by MDPI. This book was released on 2019-10-16 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed.

Entropy in Dynamical Systems

Author : Tomasz Downarowicz
Publisher : Cambridge University Press
ISBN 13 : 1139500872
Total Pages : 405 pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis Entropy in Dynamical Systems by : Tomasz Downarowicz

Download or read book Entropy in Dynamical Systems written by Tomasz Downarowicz and published by Cambridge University Press. This book was released on 2011-05-12 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon–McMillan–Breiman Theorem, the Ornstein–Weiss Return Time Theorem, the Krieger Generator Theorem and, among the newest developments, the ergodic law of series. In Part II, after an expanded exposition of classical topological entropy, the book addresses symbolic extension entropy. It offers deep insight into the theory of entropy structure and explains the role of zero-dimensional dynamics as a bridge between measurable and topological dynamics. Part III explains how both measure-theoretic and topological entropy can be extended to operators on relevant function spaces. Intuitive explanations, examples, exercises and open problems make this an ideal text for a graduate course on entropy theory. More experienced researchers can also find inspiration for further research.

Topological Entropy and Equivalence of Dynamical Systems

Author : Roy L. Adler
Publisher : American Mathematical Soc.
ISBN 13 : 0821822195
Total Pages : 90 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topological Entropy and Equivalence of Dynamical Systems by : Roy L. Adler

Download or read book Topological Entropy and Equivalence of Dynamical Systems written by Roy L. Adler and published by American Mathematical Soc.. This book was released on 1979 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this work is to prove a theorem for topological entropy analogous to Ornstein's result for measure entropy. For this a natural class of dynamical systems is needed to play the same role for topological entropy as the Bernoulli shifts do for measure entropy. Fortunately there is just such a class--the topological Markov shifts. The main result of this paper is that topological entropy along with another number, called the ergodic period, is a complete set of invariants under this new equivalence relation for the class of topological Markov shifts.

Entropy in Dynamic Systems

Author : J. A. Tenreiro Machado
Publisher :
ISBN 13 : 9783039216178
Total Pages : 1 pages
Book Rating : 4.2/5 (161 download)

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Book Synopsis Entropy in Dynamic Systems by : J. A. Tenreiro Machado

Download or read book Entropy in Dynamic Systems written by J. A. Tenreiro Machado and published by . This book was released on 2019 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed.

Combinatorial Dynamics And Entropy In Dimension One

Author : Alseda Luis
Publisher : World Scientific Publishing Company
ISBN 13 : 9814553220
Total Pages : 344 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Combinatorial Dynamics And Entropy In Dimension One by : Alseda Luis

Download or read book Combinatorial Dynamics And Entropy In Dimension One written by Alseda Luis and published by World Scientific Publishing Company. This book was released on 1993-06-04 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: In last thirty years an explosion of interest in the study of nonlinear dynamical systems occured. The theory of one-dimensional dynamical systems has grown out in many directions. One of them has its roots in the Sharkovski0 Theorem. This beautiful theorem describes the possible sets of periods of all cycles of maps of an interval into itself. Another direction has its main objective in measuring the complexity of a system, or the amount of chaos present in it. A good way of doing this is to compute topological entropy of the system. The aim of this book is to provide graduate students and researchers with a unified and detailed exposition of these developments for interval and circle maps. Many comments are added referring to related problems, and historical remarks are made. Request Inspection Copy

Dynamical Entropy in Operator Algebras

Author : Sergey Neshveyev
Publisher : Springer Science & Business Media
ISBN 13 : 3540346732
Total Pages : 294 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Dynamical Entropy in Operator Algebras by : Sergey Neshveyev

Download or read book Dynamical Entropy in Operator Algebras written by Sergey Neshveyev and published by Springer Science & Business Media. This book was released on 2006-09-22 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book addresses mathematicians and physicists, including graduate students, who are interested in quantum dynamical systems and applications of operator algebras and ergodic theory. It is the only monograph on this topic. Although the authors assume a basic knowledge of operator algebras, they give precise definitions of the notions and in most cases complete proofs of the results which are used.

Entropy of Complex Processes and Systems

Author : Eugene Barsky
Publisher : Elsevier
ISBN 13 : 012821662X
Total Pages : 308 pages
Book Rating : 4.1/5 (282 download)

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Book Synopsis Entropy of Complex Processes and Systems by : Eugene Barsky

Download or read book Entropy of Complex Processes and Systems written by Eugene Barsky and published by Elsevier. This book was released on 2020-08-17 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Entropy of Complex Processes and Systems formalizes our understanding of many complex processes, including the development of the methodology of analytical computation of complex processes as applied in many industries, such as ore processing, or more generally, in areas of natural sciences. The adequacy of the results of these calculations is confirmed by numerous experimental data obtained both on pilots and industrial facilities. The book also provides a thorough analysis of the underlying physical foundations of entropy performed from new standpoints that are of interest to theoreticians studying contemporary expositions. Provides methodologies for controlling and optimizing complex processes in branches of industry that involve transformation of materials or substances Describes entropy as the universal characteristic of a stochastic process independent of the system Introduces a new definition of entropy specifically related to dynamical phenomena

Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors

Author : Christos Volos
Publisher : MDPI
ISBN 13 : 3038978981
Total Pages : 290 pages
Book Rating : 4.0/5 (389 download)

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Book Synopsis Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors by : Christos Volos

Download or read book Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors written by Christos Volos and published by MDPI. This book was released on 2019-05-03 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors. The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.

Local Entropy Theory of a Random Dynamical System

Author : Anthony H. Dooley
Publisher : American Mathematical Soc.
ISBN 13 : 1470410559
Total Pages : 106 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Local Entropy Theory of a Random Dynamical System by : Anthony H. Dooley

Download or read book Local Entropy Theory of a Random Dynamical System written by Anthony H. Dooley and published by American Mathematical Soc.. This book was released on 2014-12-20 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors extend the notion of a continuous bundle random dynamical system to the setting where the action of R or N is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a monotone sub-additive invariant family of random continuous functions, they introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theoretic entropy. They also discuss some variants of this variational principle. The authors introduce both topological and measure-theoretic entropy tuples for continuous bundle random dynamical systems, and apply variational principles to obtain a relationship between these of entropy tuples. Finally, they give applications of these results to general topological dynamical systems, recovering and extending many recent results in local entropy theory.

Dynamical Systems

Author : Jürgen Jost
Publisher : Springer Science & Business Media
ISBN 13 : 3540288899
Total Pages : 199 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Dynamical Systems by : Jürgen Jost

Download or read book Dynamical Systems written by Jürgen Jost and published by Springer Science & Business Media. This book was released on 2005-11-24 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Breadth of scope is unique Author is a widely-known and successful textbook author Unlike many recent textbooks on chaotic systems that have superficial treatment, this book provides explanations of the deep underlying mathematical ideas No technical proofs, but an introduction to the whole field that is based on the specific analysis of carefully selected examples Includes a section on cellular automata

Invariance Entropy for Deterministic Control Systems

Author : Christoph Kawan
Publisher : Springer
ISBN 13 : 3319012886
Total Pages : 270 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Invariance Entropy for Deterministic Control Systems by : Christoph Kawan

Download or read book Invariance Entropy for Deterministic Control Systems written by Christoph Kawan and published by Springer. This book was released on 2013-10-02 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems. For the simplest possible network topology, consisting of one controller and one dynamical system connected by a digital channel, invariance entropy provides a measure for the smallest data rate above which it is possible to render a given subset of the state space invariant by means of a symbolic coder-controller pair. This concept is essentially equivalent to the notion of topological feedback entropy introduced by Nair, Evans, Mareels and Moran (Topological feedback entropy and nonlinear stabilization. IEEE Trans. Automat. Control 49 (2004), 1585–1597). The book presents the foundations of a theory which aims at finding expressions for invariance entropy in terms of dynamical quantities such as Lyapunov exponents. While both discrete-time and continuous-time systems are treated, the emphasis lies on systems given by differential equations.

Combinatorial Dynamics and Entropy in Dimension One

Author : Ll Alsedà
Publisher : World Scientific Publishing Company Incorporated
ISBN 13 : 9789810240530
Total Pages : 415 pages
Book Rating : 4.2/5 (45 download)

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Book Synopsis Combinatorial Dynamics and Entropy in Dimension One by : Ll Alsedà

Download or read book Combinatorial Dynamics and Entropy in Dimension One written by Ll Alsedà and published by World Scientific Publishing Company Incorporated. This book was released on 2000 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to two of the main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all periodic orbits of a continuous map of an interval into itself. The whole theory, which was developed based on this theorem, deals mainly with combinatorial objects, permutations, graphs, etc.: it is called combinatorial dynamics. The second direction has its main objective in measuring the complexity of a system, or the degree of "chaos" present in it. A good way of doing this is to study the topological entropy of the system. The aim of this book is to provide graduate students and researchers with a unified and detailed exposition of these developments for interval and circle maps. The second edition contains two new appendices, where an extension of the theory to tree and graph maps is presented without technical proofs.

Entropy

Author : Andreas Greven
Publisher : Princeton University Press
ISBN 13 : 1400865220
Total Pages : 376 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Entropy by : Andreas Greven

Download or read book Entropy written by Andreas Greven and published by Princeton University Press. This book was released on 2014-09-08 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of entropy arose in the physical sciences during the nineteenth century, particularly in thermodynamics and statistical physics, as a measure of the equilibria and evolution of thermodynamic systems. Two main views developed: the macroscopic view formulated originally by Carnot, Clausius, Gibbs, Planck, and Caratheodory and the microscopic approach associated with Boltzmann and Maxwell. Since then both approaches have made possible deep insights into the nature and behavior of thermodynamic and other microscopically unpredictable processes. However, the mathematical tools used have later developed independently of their original physical background and have led to a plethora of methods and differing conventions. The aim of this book is to identify the unifying threads by providing surveys of the uses and concepts of entropy in diverse areas of mathematics and the physical sciences. Two major threads, emphasized throughout the book, are variational principles and Ljapunov functionals. The book starts by providing basic concepts and terminology, illustrated by examples from both the macroscopic and microscopic lines of thought. In-depth surveys covering the macroscopic, microscopic and probabilistic approaches follow. Part I gives a basic introduction from the views of thermodynamics and probability theory. Part II collects surveys that look at the macroscopic approach of continuum mechanics and physics. Part III deals with the microscopic approach exposing the role of entropy as a concept in probability theory, namely in the analysis of the large time behavior of stochastic processes and in the study of qualitative properties of models in statistical physics. Finally in Part IV applications in dynamical systems, ergodic and information theory are presented. The chapters were written to provide as cohesive an account as possible, making the book accessible to a wide range of graduate students and researchers. Any scientist dealing with systems that exhibit entropy will find the book an invaluable aid to their understanding.

Energy and Entropy

Author : Harvey S. Leff
Publisher : CRC Press
ISBN 13 : 1000170349
Total Pages : 331 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Energy and Entropy by : Harvey S. Leff

Download or read book Energy and Entropy written by Harvey S. Leff and published by CRC Press. This book was released on 2020-08-26 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Energy is typically regarded as understandable, despite its multiple forms of storage and transfer. Entropy, however, is an enigma, in part because of the common view that it represents disorder. That view is flawed and hides entropy’s connection with energy. In fact, macroscopic matter stores internal energy, and that matter’s entropy is determined by how the energy is stored. Energy and entropy are intimately linked. Energy and Entropy: A Dynamic Duo illuminates connections between energy and entropy for students, teachers, and researchers. Conceptual understanding is emphasised where possible through examples, analogies, figures, and key points. Features: Qualitative demonstration that entropy is linked to spatial and temporal energy spreading, with equilibrium corresponding to the most equitable distribution of energy, which corresponds to maximum entropy Analysis of energy and entropy of matter and photons, with examples ranging from rubber bands, cryogenic cooling, and incandescent lamps to Hawking radiation of black holes Unique coverage of numerical entropy, the 3rd law of thermodynamics, entropic force, dimensionless entropy, free energy, and fluctuations, from Maxwell's demon to Brownian ratchets, plus attempts to violate the second law of thermodynamics

A Dynamical Systems Theory of Thermodynamics

Author : Wassim M. Haddad
Publisher : Princeton University Press
ISBN 13 : 0691190143
Total Pages : 744 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis A Dynamical Systems Theory of Thermodynamics by : Wassim M. Haddad

Download or read book A Dynamical Systems Theory of Thermodynamics written by Wassim M. Haddad and published by Princeton University Press. This book was released on 2019-06-04 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brand-new conceptual look at dynamical thermodynamics This book merges the two universalisms of thermodynamics and dynamical systems theory in a single compendium, with the latter providing an ideal language for the former, to develop a new and unique framework for dynamical thermodynamics. In particular, the book uses system-theoretic ideas to bring coherence, clarity, and precision to an important and poorly understood classical area of science. The dynamical systems formalism captures all of the key aspects of thermodynamics, including its fundamental laws, while providing a mathematically rigorous formulation for thermodynamical systems out of equilibrium by unifying the theory of mechanics with that of classical thermodynamics. This book includes topics on nonequilibrium irreversible thermodynamics, Boltzmann thermodynamics, mass-action kinetics and chemical reactions, finite-time thermodynamics, thermodynamic critical phenomena with continuous and discontinuous phase transitions, information theory, continuum and stochastic thermodynamics, and relativistic thermodynamics. A Dynamical Systems Theory of Thermodynamics develops a postmodern theory of thermodynamics as part of mathematical dynamical systems theory. The book establishes a clear nexus between thermodynamic irreversibility, the second law of thermodynamics, and the arrow of time to further unify discreteness and continuity, indeterminism and determinism, and quantum mechanics and general relativity in the pursuit of understanding the most fundamental property of the universe—the entropic arrow of time.

Smooth Ergodic Theory of Random Dynamical Systems

Author : Pei-Dong Liu
Publisher : Springer
ISBN 13 : 3540492917
Total Pages : 233 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Smooth Ergodic Theory of Random Dynamical Systems by : Pei-Dong Liu

Download or read book Smooth Ergodic Theory of Random Dynamical Systems written by Pei-Dong Liu and published by Springer. This book was released on 2006-11-14 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.

Estimation and Control over Communication Networks

Author : Alexey S. Matveev
Publisher : Springer Science & Business Media
ISBN 13 : 0817646078
Total Pages : 540 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Estimation and Control over Communication Networks by : Alexey S. Matveev

Download or read book Estimation and Control over Communication Networks written by Alexey S. Matveev and published by Springer Science & Business Media. This book was released on 2009-04-05 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic theory of estimation and control over communication networks. It develops a theory that utilizes communications, control, information and dynamical systems theory motivated and applied to advanced networking scenarios. The book establishes theoretically rich and practically important connections among modern control theory, Shannon information theory, and entropy theory of dynamical systems originated in the work of Kolmogorov. This self-contained monograph covers the latest achievements in the area. It contains many real-world applications and the presentation is accessible.