Thermodynamics : a dynamical systems approach / Wassim M. Haddad, VijaySekhar Chellaboina, Sergey G. Nersesov.

Format:

Book

Author/Creator:

Haddad, Wassim M., 1961-

Contributor:

Chellaboina, VijaySekhar, 1970-

Nersesov, Sergey G., 1976-

Series:

Princeton series in applied mathematics

Language:

English

Subjects (All):

Thermodynamics--Mathematics.

Thermodynamics.

Differentiable dynamical systems.

Physical Description:

xii, 187 pages : illustrations ; 25 cm.

Place of Publication:

Princeton : Princeton University Press, [2005]

Summary:

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 systems 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, 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.

Contents:

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

3.2 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 Thermodynamics 160.

Notes:

Includes bibliographical references (pages [175]-183) and index.

ISBN:

0691123276

OCLC:

57283951