A Dynamical Systems Theory of Thermodynamics

Name: A Dynamical Systems Theory of Thermodynamics
Brand: Princeton University Press
Price: 113.99 EUR
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Wassim M. Haddad(Autor*in)

Princeton University Press

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Erschienen am 4. Juni 2019

744 Seiten

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978-0-691-19259-8 (ISBN)

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Inhalt

Cover
Title
Copyright
Dedication
Contents
Preface
Chapter 1. Introduction
1.1 An Overview of Classical Thermodynamics
1.2 Thermodynamics and the Arrow of Time
1.3 Modern Thermodynamics, Information Theory, and Statistical Energy Analysis
1.4 Dynamical Systems
1.5 Dynamical Thermodynamics: A Postmodern Approach
1.6 A Brief Outline of the Monograph
Chapter 2. Dynamical Systems Theory
2.1 Notation, Definitions, and Mathematical Preliminaries
2.2 Stability Theory for Nonnegative Dynamical Systems
2.3 Invariant Set Stability Theorems
2.4 Semistability of Nonnegative Dynamical Systems
2.5 Stability Theory for Linear Nonnegative Dynamical Systems
2.6 Lyapunov Analysis for Continuum Dynamical Systems Defined by Semigroups
2.7 Reversibility, Irreversibility, Recoverability, and Irrecoverability
2.8 Output Reversibility in Dynamical Systems
2.9 Reversible Dynamical Systems, Volume-Preserving Flows, and Poincaré Recurrence
2.10 Poincaré Recurrence and Output Reversibility in Linear Dynamical Systems
Chapter 3. A Dynamical Systems Foundation for Thermodynamics
3.1 Introduction
3.2 Conservation of Energy and the First Law of Thermodynamics
3.3 Entropy and the Second Law of Thermodynamics
3.4 Ectropy and the Second Law of Thermodynamics
3.5 Semistability, Energy Equipartition, Irreversibility, and the Arrow of Time
3.6 Entropy Increase and the Second Law of Thermodynamics
3.7 Interconnections of Thermodynamic Systems
3.8 Monotonicity of System Energies in Thermodynamic Processes
3.9 The Second Law as a Statement of Entropy Increase
3.10 Thermodynamic Systems with Linear Energy Exchange
3.11 Semistability and Energy Equipartition in Linear Thermodynamic Models
3.12 Semistability and Energy Equipartition of Thermodynamic Systems with Directed Energy Flow
Chapter 4. Temperature Equipartition and the Kinetic Theory of Gases
4.1 Semistability and Temperature Equipartition
4.2 Boltzmann Thermodynamics
4.3 Connections to Classical Thermodynamic Energy, Entropy, and Thermal Equilibria
Chapter 5. Work, Heat, and the Carnot Cycle
5.1 On the Equivalence of Work and Heat: The First Law Revisited
5.2 Work Energy, Gibbs Free Energy, Helmholtz Free Energy, Enthalpy, and Entropy
5.3 The Carnot Cycle and the Second Law of Thermodynamics
Chapter 6. Mass-Action Kinetics and Chemical Thermodynamics
6.1 Introduction
6.2 Reaction Networks
6.3 The Law of Mass Action and the Kinetic Equations
6.4 Nonnegativity of Solutions
6.5 Realization of Mass-Action Kinetics
6.6 Reducibility of the Kinetic Equations
6.7 Stability Analysis of Linear and Nonlinear Kinetics
6.8 The Zero-Deficiency Theorem
6.9 Chemical Equilibria, Chemical Potential, and Chemical Thermodynamics
Chapter 7. Finite-Time Thermodynamics
7.1 Introduction
7.2 Finite-Time Semistability of Nonlinear Nonnegative Dynamical Systems
7.3 Homogeneity and Finite-Time Semistability
7.4 Finite-Time Energy Equipartition in Thermodynamic Systems
Chapter 8. Critical Phenomena and Continuous Phase Transitions
8.1 Introduction
8.2 Dynamical Systems with Discontinuous Vector Fields
8.3 Nonsmooth Stability Theory for Discontinuous Dynamical Systems
8.4 Energy Equipartition for Thermodynamic Systems with Discontinuous Power Balance Dynamics
Chapter 9. Thermodynamic Modeling of Discrete Dynamical Systems
9.1 Introduction
9.2 Mathematical Preliminaries
9.3 Conservation of Discrete Energy and the First Law of Thermodynamics
9.4 Nonconservation of Discrete Entropy and the Second Law of Thermodynamics
9.5 Nonconservation of Discrete Ectropy
9.6 Semistability of Discrete-Time Thermodynamic Models
9.7 Discrete Energy Equipartition
9.8 Entropy Increase and the Second Law of Thermodynamics
9.9 Discrete Temperature Equipartition
9.10 Discrete Thermodynamic Models with Linear Energy Exchange
Chapter 10. Critical Phenomena and Discontinuous Phase Transitions
10.1 Introduction
10.2 Stability Theory for Nonlinear Hybrid Nonnegative Dynamical Systems
10.3 Hybrid Thermodynamic Models
10.4 Conservation of Energy and the Hybrid First Law of Thermodynamics
10.5 Entropy and the Hybrid Second Law of Thermodynamics
10.6 Semistability and Energy Equipartition of Hybrid Thermodynamic Systems
Chapter 11. Continuum Thermodynamics
11.1 Conservation Laws in Continuum Thermodynamics
11.2 Entropy and Ectropy for Continuum Thermodynamics
11.3 Semistability and Energy Equipartition in Continuum Thermodynamics
11.4 Advection-Diffusion Dynamics
Chapter 12. Stochastic Thermodynamics: A Dynamical Systems Approach
12.1 Introduction
12.2 Stochastic Dynamical Systems
12.3 Stability Theory for Stochastic Nonnegative Dynamical Systems
12.4 Semistability of Stochastic Nonnegative Dynamical Systems
12.5 Conservation of Energy and the First Law of Thermodynamics: A Stochastic Perspective
12.6 Entropy and the Second Law of Thermodynamics
12.7 Stochastic Semistability and Energy Equipartition
Chapter 13. Relativistic Mechanics
13.1 Introduction
13.2 Relativistic Kinematics
13.3 Length Contraction and Time Dilation
13.4 Relativistic Velocity and Acceleration Transformations
13.5 Special Relativity, Minkowski Space, and the Spacetime Continuum
13.6 Relativistic Dynamics
13.7 Force, Work, and Kinetic Energy
13.8 Relativistic Momentum, Energy, Mass, and Force Transformations
13.9 The Principle of Equivalence and General Relativity
Chapter 14. Relativistic Thermodynamics
14.1 Introduction
14.2 Special Relativity and Thermodynamics
14.3 Relativity, Temperature Invariance, and the Entropy Dilation Principle
14.4 General Relativity and Thermodynamics
Chapter 15. Thermodynamic Models with Subluminal Heat Propagation Speeds
15.1 Introduction
15.2 Lyapunov Stability Theory for Time Delay Nonnegative Dynamical Systems
15.3 Invariant Set Stability Theorems
15.4 Linear and Nonlinear Nonnegative Dynamical Systems with Time Delay
15.5 Conservation of Energy for Thermodynamic Systems with Time Delay
15.6 Semistability and Equipartition of Energy for Linear Thermodynamic Systems with Time Delay
15.7 Semistability and Equipartition of Energy for Nonlinear Thermodynamic Systems with Time Delay
15.8 Monotonicity of System Energies in Thermodynamic Processes with Time Delay
Chapter 16. Conclusion
Chapter 17. Epilogue
17.1 Introduction
17.2 Thermodynamics of Living Systems
17.3 Thermodynamics and the Origin of Life
17.4 The Second Law, Entropy, Gravity, and Life
17.5 The Second Law, Health, Illness, Aging, and Death
17.6 The Second Law, Consciousness, and the Entropic Arrow of Time
17.7 Conclusion
Chapter 18. Afterword
Bibliography
Index

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