The Nature of Irreversibility: A Study of Its Dynamics and Physical Origins / Edition 1

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A dominant feature of our ordinary experience of the world is a sense of irreversible change: things lose form, people grow old, energy dissipates. On the other hand, a major conceptual scheme we use to describe the natural world, molecular dynamics, has reversibility at its core. The need to harmonize conceptual schemes and experience leads to several questions, one of which is the focus of this book. How does irreversibility at the macroscopic level emerge from the reversibility that prevails at the molecular level? Attempts to explain the emergence have emphasized probability, and assigned different probabilities to the forward and reversed directions of processes so that one direction is far more probable than the other. The conclu­ sion is promising, but the reasons for it have been obscure. In many cases the aim has been to find an explana­ tion in the nature of probability itself. Reactions to that have been divided: some think the aim is justified while others think it is absurd.

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Table of Contents

1. Introduction.- 2. The Paradoxes.- 2.1 Early Studies of Heat and Attempts to Formulate Equations of Heat Flow.- 2.2 Thompson’s 1852 Statement on Irreversibility.- 2.3 Dissipative Processes and Irreversible Processes Not Yet Distinguished.- 2.4 Statistical Notions Enter Kinetic Theory.- 2.5 Boltzmann Tries to Reduce the Second Law to Mechanics.- 2.6 The “H” Theorem and Loschmidt’s Reversibility Paradox.- 2.7 The Reversibility Paradox Rediscovered.- 2.8 Boltzmann’s Philosophy of Science.- 2.9 The Boltzmann-Planck Debate.- 2.10 Ehrenfests and the Problem of Irreversibility.- 3. The Applications.- 3.1 Transport Rates Determined by Mean Free Paths.- 3.2 Transport Rates Determined by the Boltzmann Equation.- 4. Return to the Paradoxes.- 4.1 The Loss of Information.- 4.2 Microscopic Reversibility.- 4.3 The Role of Recent Equilibrium.- 4.4 Molecular Chaos and the BBGKY Theory.- 4.5 Later Developments.- 5. Various Kinds of Irreversibility.- 5.1 Inertial Irreversibility.- 5.2 Temporal Irreversibility.- 5.3 Exclusion Irreversibility.- 5.4 Mixing the Criteria: Thermodynamic Irreversibility.- 5.5 Mixing the Criteria: Paradoxical Irreversibility.- 5.6 Refinements: de Facto and Nomological Irreversibility.- 5.7 Statistical Irreversibility: Necessarily de Facto.- 6. Proposed Origins of Irreversibility.- 6.1 Probabilistic Origins.- 6.2 Mechanical Origins.- 7. The Origin of Exclusion Irreversibility.- 7.1 The Simplest Newtonian Models.- 7.2 The Role of Time Scales.- 7.3 Exclusion and Dissipation.- 7.4 The Principle of Recent Equilibrium.- 7.5 A Reflection.- 8. Irreversibility in Fluid Dynamics.- 8.1 The Fluid Concept.- 8.2 Fluid Processes.- 8.3 Fluid Equations.- 8.4 Fundamental Equations of Change.- 8.5 Shastic Equations of Change.- 8.6 Simple Equations of Flux.- 8.7 Complex Equations of Flux.- 8.8 Equations of Equilibrium.- 9. Irreversibility in Statistical Mechanics.- 9.1 The Method of Statistical Mechanics.- 9.2 Generalization to Systems of Interacting Particles.- 9.3 Generalization to a Continuum of States.- 9.4 The Liouville Theorem.- 9.5 Joining Statistics and Mechanics: The One-Particle Approximation.- 9.6 Complex Equations of Flux in the One-Particle Approximation.- 9.7 The Two-Particle Approximation.- 9.8 Higher Approximations.- 10. Irreversibility in Quantum statistical Mechanics.- 10.1 The Schrödinger Equation.- 10.2 The One-Particle Approximation.- 10.3 The Two-Particle Approximation.- 10.4 The Chemical Approximation.- 11. On Alternative Approaches.- Appendix - Some Reflections on Time and Temporality.- Notes.- References.- Name Index.

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