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Dynamical Systems Theory of Thermodynamics [Kõva köide]

  • Formaat: Hardback, 744 pages, kõrgus x laius: 254x178 mm, 20 b/w illus.
  • Sari: Princeton Series in Applied Mathematics
  • Ilmumisaeg: 04-Jun-2019
  • Kirjastus: Princeton University Press
  • ISBN-10: 0691190143
  • ISBN-13: 9780691190143
Teised raamatud teemal:
Dynamical Systems Theory of ThermodynamicsSuurem pilt
  • Formaat: Hardback, 744 pages, kõrgus x laius: 254x178 mm, 20 b/w illus.
  • Sari: Princeton Series in Applied Mathematics
  • Ilmumisaeg: 04-Jun-2019
  • Kirjastus: Princeton University Press
  • ISBN-10: 0691190143
  • ISBN-13: 9780691190143
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780691190143.html

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.

Arvustused

This remarkable book studies thermodynamics within the framework of dynamical systems theory. A major contribution by any standard, it is a gem in the tiara of books being written by one of the most prolific, deep-thinking, and insightful researchers working today.Frank Lewis, University of Texas, Arlington Haddad develops an original mathematical framework for thermodynamics deeply rooted in modern systems theory, threading postulates and analyses of a science that has evolved from the seemingly mundane quest for efficiency in steam engines to the flow of time and the workings of the cosmos and life itself. He succeeds in presenting an all-encompassing treatise, from the early works of Carnot and Clausius to the insights of relativity and the conundrum of the time arrow, in a lucid exposition that systematically details a rigorous base for future generations of scientists and theorists.Tryphon Georgiou, University of California, Irvine "By applying ideas and techniques from compartmental systems theory, Haddads treatise places thermodynamics on a solid foundation for the twenty-first century."Dennis Bernstein, University of Michigan "This effective blend of thermodynamics and the theory of dynamical systems provides a unified, coherent, and mathematically accurate framework that is currently missing in the literature. This is a significant contribution to several fields spanning dynamical systems, mathematics, physics, chemistry, and more. It will provide the underlying foundation for additional research and conceptual understanding of physical phenomena."Kyriakos G. Vamvoudakis, Georgia Institute of Technology

Preface xv
Chapter 1 Introduction 1(38)
1.1 An Overview of Classical Thermodynamics
1(14)
1.2 Thermodynamics and the Arrow of Time
15(4)
1.3 Modern Thermodynamics, Information Theory, and Statistical Energy Analysis
19(6)
1.4 Dynamical Systems
25(4)
1.5 Dynamical Thermodynamics: A Postmodern Approach
29(5)
1.6 A Brief Outline of the Monograph
34(5)
Chapter 2 Dynamical Systems Theory 39(76)
2.1 Notation, Definitions, and Mathematical Preliminaries
39(6)
2.2 Stability Theory for Nonnegative Dynamical Systems
45(3)
2.3 Invariant Set Stability Theorems
48(6)
2.4 Semistability of Nonnegative Dynamical Systems
54(9)
2.5 Stability Theory for Linear Nonnegative Dynamical Systems
63(8)
2.6 Lyapunov Analysis for Continuum Dynamical Systems Defined by Semigroups
71(7)
2.7 Reversibility, Irreversibility, Recoverability, and Irrecoverability
78(7)
2.8 Output Reversibility in Dynamical Systems
85(11)
2.9 Reversible Dynamical Systems, Volume-Preserving Flows, and Poincare Recurrence
96(10)
2.10 Poincare Recurrence and Output Reversibility in Linear Dynamical Systems
106(9)
Chapter 3 A Dynamical Systems Foundation for Thermodynamics 115(84)
3.1 Introduction
115(2)
3.2 Conservation of Energy and the First Law of Thermodynamics
117(9)
3.3 Entropy and the Second Law of Thermodynamics
126(17)
3.4 Ectropy and the Second Law of Thermodynamics
143(8)
3.5 Semistability, Energy Equipartition, Irreversibility, and the Arrow of Time
151(11)
3.6 Entropy Increase and the Second Law of Thermodynamics
162(3)
3.7 Interconnections of Thermodynamic Systems
165(6)
3.8 Monotonicity of System Energies in Thermodynamic Processes
171(4)
3.9 The Second Law as a Statement of Entropy Increase
175(5)
3.10 Thermodynamic Systems with Linear Energy Exchange
180(5)
3.11 Semistability and Energy Equipartition in Linear Thermodynamic Models
185(4)
3.12 Semistability and Energy Equipartition of Thermodynamic Systems with Directed Energy Flow
189(10)
Chapter 4 Temperature Equipartition and the Kinetic Theory of Gases 199(24)
4.1 Semistability and Temperature Equipartition
199(7)
4.2 Boltzmann Thermodynamics
206(3)
4.3 Connections to Classical Thermodynamic Energy, Entropy, and Thermal Equilibria
209(14)
Chapter 5 Work, Heat, and the Carnot Cycle 223(24)
5.1 On the Equivalence of Work and Heat: The First Law Revisited
223(11)
5.2 Work Energy, Gibbs Free Energy, Helmholtz Free Energy, Enthalpy, and Entropy
234(8)
5.3 The Carnot Cycle and the Second Law of Thermodynamics
242(5)
Chapter 6 Mass-Action Kinetics and Chemical Thermodynamics 247(42)
6.1 Introduction
247(2)
6.2 Reaction Networks
249(2)
6.3 The Law of Mass Action and the Kinetic Equations
251(4)
6.4 Nonnegativity of Solutions
255(2)
6.5 Realization of Mass-Action Kinetics
257(3)
6.6 Reducibility of the Kinetic Equations
260(4)
6.7 Stability Analysis of Linear and Nonlinear Kinetics
264(4)
6.8 The Zero-Deficiency Theorem
268(13)
6.9 Chemical Equilibria, Chemical Potential, and Chemical Thermodynamics
281(8)
Chapter 7 Finite-Time Thermodynamics 289(18)
7.1 Introduction
289(1)
7.2 Finite-Time Semistability of Nonlinear Nonnegative Dynamical Systems
290(4)
7.3 Homogeneity and Finite-Time Semistability
294(8)
7.4 Finite-Time Energy Equipartition in Thermodynamic Systems
302(5)
Chapter 8 Critical Phenomena and Continuous Phase Transitions 307(24)
8.1 Introduction
307(2)
8.2 Dynamical Systems with Discontinuous Vector Fields
309(3)
8.3 Nonsmooth Stability Theory for Discontinuous Dynamical Systems
312(12)
8.4 Energy Equipartition for Thermodynamic Systems with Discontinuous Power Balance Dynamics
324(7)
Chapter 9 Thermodynamic Modeling of Discrete Dynamical Systems 331(52)
9.1 Introduction
331(1)
9.2 Mathematical Preliminaries
332(11)
9.3 Conservation of Discrete Energy and the First Law of Thermodynamics
343(4)
9.4 Nonconservation of Discrete Entropy and the Second Law of Thermodynamics
347(7)
9.5 Nonconservation of Discrete Ectropy
354(5)
9.6 Semistability of Discrete-Time Thermodynamic Models
359(6)
9.7 Discrete Energy Equipartition
365(1)
9.8 Entropy Increase and the Second Law of Thermodynamics
365(2)
9.9 Discrete Temperature Equipartition
367(5)
9.10 Discrete Thermodynamic Models with Linear Energy Exchange
372(11)
Chapter 10 Critical Phenomena and Discontinuous Phase Transitions 383(38)
10.1 Introduction
383(1)
10.2 Stability Theory for Nonlinear Hybrid Nonnegative Dynamical Systems
384(14)
10.3 Hybrid Thermodynamic Models
398(5)
10.4 Conservation of Energy and the Hybrid First Law of Thermodynamics
403(6)
10.5 Entropy and the Hybrid Second Law of Thermodynamics
409(5)
10.6 Semistability and Energy Equipartition of Hybrid Thermodynamic Systems
414(7)
Chapter 11 Continuum Thermodynamics 421(40)
11.1 Conservation Laws in Continuum Thermodynamics
421(10)
11.2 Entropy and Ectropy for Continuum Thermodynamics
431(12)
11.3 Semistability and Energy Equipartition in Continuum Thermodynamics
443(15)
11.4 Advection-Diffusion Dynamics
458(3)
Chapter 12 Stochastic Thermodynamics: A Dynamical Systems Approach 461(62)
12.1 Introduction
461(3)
12.2 Stochastic Dynamical Systems
464(7)
12.3 Stability Theory for Stochastic Nonnegative Dynamical Systems
471(8)
12.4 Semistability of Stochastic Nonnegative Dynamical Systems
479(10)
12.5 Conservation of Energy and the First Law of Thermodynamics: A Stochastic Perspective
489(10)
12.6 Entropy and the Second Law of Thermodynamics
499(19)
12.7 Stochastic Semistability and Energy Equipartition
518(5)
Chapter 13 Relativistic Mechanics 523(44)
13.1 Introduction
523(8)
13.2 Relativistic Kinematics
531(9)
13.3 Length Contraction and Time Dilation
540(2)
13.4 Relativistic Velocity and Acceleration Transformations
542(3)
13.5 Special Relativity, Minkowski Space, and the Spacetime Continuum
545(7)
13.6 Relativistic Dynamics
552(3)
13.7 Force, Work, and Kinetic Energy
555(3)
13.8 Relativistic Momentum, Energy, Mass, and Force Transformations
558(2)
13.9 The Principle of Equivalence and General Relativity
560(7)
Chapter 14 Relativistic Thermodynamics 567(24)
14.1 Introduction
567(5)
14.2 Special Relativity and Thermodynamics
572(9)
14.3 Relativity, Temperature Invariance, and the Entropy Dilation Principle
581(6)
14.4 General Relativity and Thermodynamics
587(4)
Chapter 15 Thermodynamic Models with Subluminal Heat Propagation Speeds 591(42)
15.1 Introduction
591(3)
15.2 Lyapunov Stability Theory for Time Delay Nonnegative Dynamical Systems
594(4)
15.3 Invariant Set Stability Theorems
598(4)
15.4 Linear and Nonlinear Nonnegative Dynamical Systems with Time Delay
602(6)
15.5 Conservation of Energy for Thermodynamic Systems with Time Delay
608(2)
15.6 Semistability and Equipartition of Energy for Linear Thermodynamic Systems with Time Delay
610(4)
15.7 Semistability and Equipartition of Energy for Nonlinear Thermodynamic Systems with Time Delay
614(14)
15.8 Monotonicity of System Energies in Thermodynamic Processes with Time Delay
628(5)
Chapter 16 Conclusion 633(8)
Chapter 17 Epilogue 641(30)
17.1 Introduction
641(2)
17.2 Thermodynamics of Living Systems
643(7)
17.3 Thermodynamics and the Origin of Life
650(3)
17.4 The Second Law, Entropy, Gravity, and Life
653(3)
17.5 The Second Law, Health, Illness, Aging, and Death
656(3)
17.6 The Second Law, Consciousness, and the Entropic Arrow of Time
659(7)
17.7 Conclusion
666(5)
Chapter 18 Afterword 671(6)
Bibliography 677(34)
Index 711
Wassim M. Haddad is a professor in the School of Aerospace Engineering, the David Lewis Chair in Dynamical Systems and Control, and chair of the Flight Mechanics and Control Discipline, all at the Georgia Institute of Technology, where he also holds a joint appointment in the School of Electrical and Computer Engineering. He is the coauthor of numerous books, including Stability and Control of Large-Scale Dynamical Systems and Nonlinear Dynamical Systems and Control (both Princeton).