Thermodynamics : a dynamical systems approach

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.

Author Notes

VijaySekhar Chellaboina is Associate Professor in the Department of Mechanical, Aerospace, and Biomedical Engineering at the University of Tennessee.

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

Available:*

On Order

Summary

Summary

Author Notes

Table of Contents