Time’s Arrow: The Origins of Thermodynamic Behavior

1. Front Matter

   Pages i-xv

   PDF

2. Starters

   • Michael C. Mackey

   Pages 1-8

3. Maximal Entropy Principles

   • Michael C. Mackey

   Pages 9-20

4. Invertible and Noninvertible Systems

   • Michael C. Mackey

   Pages 21-38

5. Ergodicity and Unique Equilibria

   • Michael C. Mackey

   Pages 39-57

6. Mixing

   • Michael C. Mackey

   Pages 58-69

7. Asymptotic Periodicity and Entropy Evolution

   • Michael C. Mackey

   Pages 70-88

8. Global Evolution of Entropy

   • Michael C. Mackey

   Pages 89-102

9. Coarse Graining

   • Michael C. Mackey

   Pages 103-109

10. Traces and Factors

    • Michael C. Mackey

    Pages 110-114

11. Open Discrete Time Systems

    • Michael C. Mackey

    Pages 115-139

12. Open Continuous Time Systems

    • Michael C. Mackey

    Pages 140-158

13. Back Matter

    Pages 159-175

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The Second Law of Thermodynamics has been called the most important law of nature: It is the law that gives a direction to processes that is not inherent in the laws of motion, that says the state of the universe is driven to thermal equilibrium. Its mathematical formulation is simple: The entropy of a closed system cannot decrease. Since the recognition that macroscopic phenomena have an atomic basis, it has remained a fundamental problem to reconcile the increase of entropy with the known reversibility of all the laws of microscopic physics. Professor Michael Mackey of McGill University here explores the dynamical basis for the Second Law, that is, he seeks to illuminate the fundamental dynamical properties required for the construction of a successful statistical mechanics. Aimed at physicists and applied mathematicians with an interest in the foundations of statistical mechanics, the book includes such new material as: a demonstration that the black body radiation law can be deduced from maximal entropy principles; a discussion of sufficient conditions for the existence of at least one state of thermodynamic equilibrium; a description of the behavior of entropy in asymptotically periodic systems; a necessary and sufficient condition for the evolution of entropy to a global maximum; and a presen- tation of the three main types of ergodic theorems and their proofs. He also explores the potential role of incomplete knowledge of dynamical variables, measurement imprecision, and the effects of noise in giving rise to entropy increases.

• Universe
• behavior
• dynamics
• entropy
• evolution
• mechanics
• noise
• physics
• radiation
• statistical mechanics
• system
• thermodynamics

• Center for Nonlinear Dynamics in Physiology and Medicine, McGill University, Montreal, Canada

  Michael C. Mackey

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