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A Dynamical Systems Approach
Wassim M. Haddad, Vijay Sekhar Chellaboina, & Sergey G. Nersesov

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Preface ix
Chapter 1: Introduction 1
1.1 An Overview of Thermodynamics 1
1.2 System Thermodynamics 11
1.3 A Brief Outline of the Monograph 14
Chapter 2: Dynamical System Theory 17
2.1 Notation, Definitions, and Mathematical Preliminaries 17
2.2 Stability Theory for Nonnegative Dynamical Systems 20
2.3 Reversibility, Irreversibility, Recoverability, and Irrecoverability 27
2.4 Reversible Dynamical Systems, Volume-Preserving Flows, and Poincaré Recurrence 34
Chapter 3: A Systems Foundation for Thermodynamics 45
3.1 Introduction 45
3.2 Conservation of Energy and the First Law of Thermodynamics 46
3.3 Entropy and the Second Law of Thermodynamics 55
3.4 Ectropy 72
3.5 Semistability, Energy Equipartition, Irreversibility, and the Arrow of Time 81
3.6 Entropy Increase and the Second Law of Thermodynamics 89
3.7 Interconnections of Thermodynamic Systems 91
3.8 Monotonicity of System Energies in Thermodynamic Processes 98
Chapter 4: Temperature Equipartition and the Kinetic Theory of Gases
103 4.1 Semistability and Temperature Equipartition 103
4.2 Boltzmann Thermodynamics 110
Chapter 5: Work, Heat, and the Carnot Cycle 115
5.1 On the Equivalence of Work and Heat: The First Law Revisited 115
5.2 The Carnot Cycle and the Second Law of Thermodynamics 126
Chapter 6: Thermodynamic Systems with Linear Energy Exchange 131
6.1 Linear Thermodynamic System Models 131
6.2 Semistability and Energy Equipartition in Linear Thermodynamic Models 136
Chapter 7: Continuum Thermodynamics 141
7.1 Conservation Laws in Continuum Thermodynamics 141
7.2 Entropy and Ectropy for Continuum Thermodynamics 148
7.3 Semistability and Energy Equipartition in Continuum Thermo-dynamics 160
Chapter 8: Conclusion 169
Bibliography 175
Index 185

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File created: 4/27/2015

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