Time's Arrow

The Origins of Thermodynamic Behavior

By: Michael C. Mackey

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Paperback | 17 November 2003

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175 Pages

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Written by a well-known professor of physiology at McGill University, this text presents an informative exploration of the basis of the Second Law of Thermodynamics, detailing the fundamental dynamic properties behind the construction of statistical mechanics.
Topics include maximal entropy principles; invertible and noninvertible systems; ergodicity and unique equilibria; asymptotic periodicity and entropy evolution; and open discrete and continuous time systems. The author demonstrates that the black body radiation law can be deduced from maximal entropy principles; discusses sufficient conditions for the existence of at least one state of thermodynamic equilibrium; describes the behavior of entropy in asymptotically periodic systems and the necessary and sufficient condition for the evolution of entropy to a global maximum; and presents the three main types of ergodic theorems and theory proofs. He also explores the potential of incomplete knowledge of dynamical variables, measurement imprecision, and the effects of noise in entropy increases.
Geared toward physicists and applied mathematicians with an interest in the foundations of statistical mechanics, this text is suitable for advanced undergraduate and graduate courses.

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Preface	p. ix
Starters	p. 1
Thermodynamic Systems	p. 1
Dynamics	p. 2
Thermodynamic States	p. 4
Boltzmann-Gibbs Entropy	p. 5
Summary	p. 8
Maximal Entropy Principles	p. 9
Microcanonical Ensembles	p. 9
Canonical Ensembles	p. 11
The Thermodynamic Connection	p. 12
Boltzmann and Other Statistics	p. 16
Blackbody Radiation	p. 18
General Entropy Maxima	p. 19
Maximal Entropy Principles	p. 20
Summary	p. 20
Invertible and Noninvertible Systems	p. 21
Markov Operators	p. 21
Conditional Entropy	p. 27
Existence of Equilibria	p. 34
Summary	p. 37
Ergodicity and Unique Equilibria	p. 39
Frobenius-Perron Operator	p. 39
The Koopman Operator	p. 43
Recurrence	p. 45
Densities and Flows	p. 46
Ergodicity	p. 48
Summary	p. 57
Mixing	p. 58
Mixing	p. 58
Kolmogorov Systems	p. 66
The Decay of Correlations	p. 67
Summary	p. 68
Asymptotic Periodicity and Entropy Evolution	p. 70
Asymptotic Periodicity	p. 70
Asymptotic Periodicity Illustrated	p. 75
The Weak Form of the Second Law	p. 80
Asymptotic Periodicity and Correlations	p. 86
Summary	p. 88
Global Evolution of Entropy	p. 89
Exactness	p. 89
The Strong Form of the Second Law	p. 98
Summary	p. 101
Coarse Graining	p. 103
Coarse Grained Entropy	p. 103
Coarse Graining of Mixing Systems	p. 106
Sampling	p. 107
Summary	p. 109
Traces and Factors	p. 110
Traces	p. 110
Factors	p. 112
Coarse Graining and Traces	p. 113
Summary	p. 114
Open Discrete Time Systems	p. 115
An Operator Equation	p. 116
Loosely Coupled Systems	p. 117
Strongly Coupled Systems	p. 120
Asymptotic Periodicity and Additive Perturbations	p. 123
Exactness and Additive Perturbations	p. 129
Parametric Perturbations	p. 131
Markov Operators and Deterministic Processes	p. 136
Summary	p. 138
Open Continuous Time Systems	p. 140
Wiener Processes and Stochastic Differential Equations	p. 140
The Fokker-Planck Equation	p. 142
Solutions of the Fokker-Planck Equation	p. 145
The Behavior of Entropy	p. 148
Phase Transitions and Additive Perturbations	p. 151
Parametric Perturbations and Phase Transitions	p. 156
Summary	p. 158
References	p. 159
Index	p. 167
Table of Contents provided by Ingram. All Rights Reserved.

Time's Arrow

The Origins of Thermodynamic Behavior

At a Glance

Paperback

Shipping

How to return your order

Defective items

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