Description
Book SynopsisPlaces thermodynamics on a system-theoretic foundation so as to harmonize it with classical mechanics. This book suggests that 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.
Trade ReviewWassim Haddad, Winner of the 2014 Pendray Aerospace Literature Award, American Institute of Aeronautics and Astronautics "The mathematical approach taken by the authors, as originally initiated by C. Caratheodory on the advice of Max Born, results in a book that makes a fundamental contribution to the field. The main emphasis is on the notion of large-scale dynamical systems applied to the multitude of small objects contained in the macroscale description. Indeed, thermodynamics is the dynamics of an extremely large number of objects numbering on the order of Avogadro's number. That some definite results arise from that setting is the marvel of it all."--Gerard A. Maugin, IEEE Control Systems "This is an original theory with many attractive features and which captures the known statements from classical thermodynamics, avoiding at the same time imprecise formulations. The techniques are based on dynamical systems and control theory, which is unusual in the field, but the presentation is precise and well crafted."--Manuel Portilheiro, Mathematical Reviews
Table of ContentsPreface 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 Poincare 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
