A Dynamical Systems Theory Of Thermodynamics
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A Dynamical Systems Theory Of Thermodynamics
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Author : Wassim M. Haddad
language : en
Publisher: Princeton University Press
Release Date : 2019-06-04
A Dynamical Systems Theory Of Thermodynamics written by Wassim M. Haddad and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-04 with Mathematics categories.
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.
Thermodynamics
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Author : Wassim M. Haddad
language : en
Publisher: Princeton University Press
Release Date : 2009-01-10
Thermodynamics written by Wassim M. Haddad and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-10 with Science categories.
This book places thermodynamics on a system-theoretic foundation so as to harmonize it with classical mechanics. Using the highest standards of exposition and rigor, the authors develop a novel formulation of thermodynamics that can be viewed as a moderate-sized system theory as compared to statistical thermodynamics. This middle-ground theory involves deterministic large-scale dynamical system models that bridge the gap between classical and statistical thermodynamics. The authors' theory is motivated by the fact that a discipline as cardinal as thermodynamics--entrusted with some of the most perplexing secrets of our universe--demands far more than physical mathematics as its underpinning. Even though many great physicists, such as Archimedes, Newton, and Lagrange, have humbled us with their mathematically seamless eurekas over the centuries, this book suggests that a great many physicists and engineers who have developed the theory of thermodynamics seem to have forgotten that mathematics, when used rigorously, is the irrefutable pathway to truth. This book uses system theoretic ideas to bring coherence, clarity, and precision to an extremely important and poorly understood classical area of science.
Thermodynamic Formalism And Holomorphic Dynamical Systems
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Author : Michel Zinsmeister
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Thermodynamic Formalism And Holomorphic Dynamical Systems written by Michel Zinsmeister and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The purpose of thermodynamics and statistical physics is to understand the equilibrium of a gas or the different states of matter. To understand the strange fractal sets appearing when one iterates a quadratic polynomial is one of the goals of the theory of holomorphic dynamical systems. These two theories are strongly linked: The laws of thermodynamics happen to be an extremely powerful tool for understanding the objects of holomorphic dynamical systems. A "thermodynamic formalism" has been developed, bringing together notions that are a priori unrelated. While the deep reasons of this parallelism remain unknown, the goal of this book is to describe this formalism both from the physical and mathematical point of view in order to understand how it works and how useful it can be. This translation is a slightly revised version of the original French edition. The main changes are in Chapters 5 and 6 and consist of clarification of some proofs and a new presentation of the basics in iteration of polynomials.
Energy Flow Theory Of Nonlinear Dynamical Systems With Applications
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Author : Jing Tang Xing
language : en
Publisher: Springer
Release Date : 2015-05-28
Energy Flow Theory Of Nonlinear Dynamical Systems With Applications written by Jing Tang Xing and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-28 with Technology & Engineering categories.
This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as an undergraduate or graduate textbook or a comprehensive source for scientists, researchers and engineers, providing the statement of the art on energy flow or power flow theory and methods.
Nonnegative And Compartmental Dynamical Systems
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Author : Wassim M. Haddad
language : en
Publisher: Princeton University Press
Release Date : 2010-01-04
Nonnegative And Compartmental Dynamical Systems written by Wassim M. Haddad and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-04 with Mathematics categories.
This comprehensive book provides the first unified framework for stability and dissipativity analysis and control design for nonnegative and compartmental dynamical systems, which play a key role in a wide range of fields, including engineering, thermal sciences, biology, ecology, economics, genetics, chemistry, medicine, and sociology. Using the highest standards of exposition and rigor, the authors explain these systems and advance the state of the art in their analysis and active control design. Nonnegative and Compartmental Dynamical Systems presents the most complete treatment available of system solution properties, Lyapunov stability analysis, dissipativity theory, and optimal and adaptive control for these systems, addressing continuous-time, discrete-time, and hybrid nonnegative system theory. This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers, as well as for researchers and graduate students who want to understand the behavior of nonnegative and compartmental dynamical systems that arise in areas such as biomedicine, demographics, epidemiology, pharmacology, telecommunications, transportation, thermodynamics, networks, heat transfer, and power systems.
The Complexity Of Dynamical Systems
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Author : Johan Dubbeldam
language : en
Publisher: John Wiley & Sons
Release Date : 2011-02-21
The Complexity Of Dynamical Systems written by Johan Dubbeldam and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-21 with Science categories.
Written by recognized experts, this edited book covers recent theoretical, experimental and applied issues in the growing fi eld of Complex Systems and Nonlinear Dynamics. It is divided into two parts, with the first section application based, incorporating the theory of bifurcation analysis, numerical computations of instabilities in dynamical systems and discussing experimental developments. The second part covers the broad category of statistical mechanics and dynamical systems. Several novel exciting theoretical and mathematical insights and their consequences are conveyed to the reader.
Network Information Systems
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Author : Wassim M. Haddad
language : en
Publisher: SIAM
Release Date : 2023-06-06
Network Information Systems written by Wassim M. Haddad and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-06 with Mathematics categories.
This text presents a unique treatment of network control systems. Drawing from fundamental principles of dynamical systems theory and dynamical thermodynamics, the authors develop a continuous-time, discrete-time, and hybrid dynamical system and control framework for linear and nonlinear large-scale network systems. The proposed framework extends the concepts of energy, entropy, and temperature to undirected and directed information networks. Continuous-time, discrete-time, and hybrid thermodynamic principles are used to design distributed control protocol algorithms for static and dynamic networked systems in the face of system uncertainty, exogenous disturbances, imperfect system network communication, and time delays. Network Information Systems: A Dynamical Systems Approach is written for applied mathematicians, dynamical systems theorists, control theorists, and engineers. Researchers and graduate students in a variety of fields who seek a fundamental understanding of the rich behavior of controlled large-scale network systems will also find this book useful. This book can be used for a first course on control design of large-scale network systems, such as control protocols for network systems, network information systems, a dynamical systems approach to network systems, and network thermodynamic systems. The prerequisites are a first course in nonlinear systems theory and a first course in advanced (multivariable) calculus.
Equidistribution Of Dynamical Systems Time Quantitative Second Law
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Author : Jozsef Beck
language : en
Publisher: World Scientific
Release Date : 2020-10-05
Equidistribution Of Dynamical Systems Time Quantitative Second Law written by Jozsef Beck and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-05 with Mathematics categories.
We know very little about the time-evolution of many-particle dynamical systems, the subject of our book. Even the 3-body problem has no explicit solution (we cannot solve the corresponding system of differential equations, and computer simulation indicates hopelessly chaotic behaviour). For example, what can we say about the typical time evolution of a large system starting from a stage far from equilibrium? What happens in a realistic time scale? The reader's first reaction is probably: What about the famous Second Law (of thermodynamics)?Unfortunately, there are plenty of notorious mathematical problems surrounding the Second Law. (1) How to rigorously define entropy? How to convert the well known intuitions (like 'disorder' and 'energy spreading') into precise mathematical definitions? (2) How to express the Second Law in forms of a rigorous mathematical theorem? (3) The Second Law is a 'soft' qualitative statement about entropy increase, but does not say anything about the necessary time to reach equilibrium.The object of this book is to answer questions (1)-(2)-(3). We rigorously prove a Time-Quantitative Second Law that works on a realistic time scale. As a by product, we clarify the Loschmidt-paradox and the related reversibility/irreversibility paradox.
Thermodynamics Kinetics Of Dynamic Systems
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Author : Federico Noguerra
language : en
Publisher:
Release Date : 2016-04-01
Thermodynamics Kinetics Of Dynamic Systems written by Federico Noguerra and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-01 with categories.
"Thermodynamics is the study of heat, ""thermo,"" and work, ""dynamics."" Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. In particular, it describes how thermal energy is converted to and from other forms of energy and how it affects matter. It was born in the 19th century as scientists were first discovering how to build and operate steam engines. Thermodynamics deals only with the large scale response of a system which we can observe and measure in experiments. Small scale gas interactions are described by the kinetic theory of gases. The methods complement each other; some principles are more easily understood in terms of thermodynamics and some principles are more easily explained by kinetic theory. Thermodynamics, then, is concerned with several properties of matter; foremost among these is heat. Heat is energy transferred between substances or systems due to a temperature difference between them. As a form of energy, heat is conserved, i.e., it cannot be created or destroyed. It can, however, be transferred from one place to another. Heat can also be converted to and from other forms of energy. Thermodynamics - Kinetics of Dynamic Systems, being concentrated on a wide range of applications of thermodynamics, gathers a series of contributions by the scientists in the world, gathered in a systematic manner. It can be used in post-graduate courses for students and researchers to whom the thermodynamics is one of the areas of interest. "
Dynamical Systems A Renewal Of Mechanism Contennial Of Georges David Birkhoff
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Author : Simon Diner
language : en
Publisher: World Scientific
Release Date : 1986-09-01
Dynamical Systems A Renewal Of Mechanism Contennial Of Georges David Birkhoff written by Simon Diner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-09-01 with Mathematics categories.
This book commemorates the centenary of the birth of Georges David Birhoff, the father of the theory of Dynamical Systems. It consists of a volume of dedicated papers, reflecting the intellectual revolution of his work. This book is divided into four parts: Fundamental Paradigms — Chaos, Turbulence, Attractors, Bifurcations; Dynamical Systems and Microphysics; Self-Organization and Biological Dynamical Systems; Epistemology and History.