The Concept of Probability in Statistical Physics

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ISBN: 9780521621281 | 0521621283
Cover: Hardcover
Copyright: 7/13/1999

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Foundational issues in statistical mechanics and the more general question of how probability is to be understood in the context of physical theories are both areas that have been neglected by philosophers of physics. This book fills an important gap in the literature by providing the most systematic study to date of how to interpret probabilistic assertions in the context of statistical mechanics. The book will be of particular interest to philosophers of science, physicists and mathematicians interested in foundational issues, and also to historians of science.

Introduction

(9)

The Neo-Laplacian Approach to Statistical Mechanics

(54)

The Introduction of Statistics into Physics

(5)

Maxwell's Second Derivation of the Velocity Distribution

(3)

Boltzmann's Atomism and Its Critics

(3)

On Gibbs's Conception of SM and Some Attempts to Revise It

(9)

The Predictive Approach to SM

(7)

The Concept of Equilibrium

(4)

The Principle of Maximum Entropy

(4)

The H-Theorem

(4)

The Canonical Distribution Obtained by the Use of a Variational Principle

(2)

Jaynes and Gibbs

(4)

A Critique of Jaynes's Theory

(6)

Subjectivism Versus Pragmatism in the Foundations of SM

(3)

Subjectivism and the Ergodic Approach

(70)

The Atomistic Conception in Light of the Research on the Brownian Motion

(6)

The Conceptual Foundations of the Statistical Approach to Mechanics by P. and T. Ehrenfest

(3)

An Introduction to Ergodic Theory

(7)

Frequentism and the Ergodic Approach

(3)

Application of the Ergodic Theory to the Theory of Hamiltonian Systems

(4)

Has the Ergodic Approach Solved the Foundational Problems of SM?

(9)

A Subjectivist Version of the Ergodic Approach

(11)

Status of the Stationarity Assumption from a Subjectivist Point of View

107

(8)

SM as an Inductive Consistency Argument

115

(6)

The Ising--Lenz Theory as an Example of an Inductive Consistency Argument

121

(11)

Beyond Inductive Consistency: The Results of Sinai

132

(2)

The Haar Measure

134

(17)

Group-Invariant Measures

134

(3)

The Construction of the Haar Measure

137

(1)

Interpretation and Application of the Notion of Congruence

138

(4)

Weak Congruence Relations

142

(2)

Hopf's Notion of Equivalence by Decomposition

144

(3)

Maxwell's Conception of the Ergodicity Assumption

147

(2)

The Elimination of Probability

149

(2)

Measure and Topology in Statistical mechanics

151

(39)

The Naturalist Conception of Physics

151

(5)

Some Topological Concepts

156

(3)

Topological Dynamics as a Foundation for Mechanics

159

(7)

Probabilistic Versus Topological Versions of the Inductive Inference

166

(5)

The Topological-Dynamical Approach to SM

171

(6)

Instability and Regional Transitivity

177

(4)

Can SM Be Formulated Using Only Topological Concepts?

181

(3)

On the Physical Interpretation of the Notion of Distance

184

(6)

Three Solutions

190

(27)

The Puzzle Concerning the Concept of Probability in SM

190

(2)

The Extension of the Subjectivist Framework

192

(8)

Reformulation of the Aims of the Ergodic Approach

200

(7)

Pragmatist Foundations of SM

207

(7)

A Conclusion

214

(3)

Appendix I: Mathematical Preliminaries

217

(7)

I.1. Elementary Measure Theory

217

(1)

I.2. Measurable Functions and Integration

218

(1)

I.3. Topological Spaces

218

(3)

I.4. Continuous Functions

221

(1)

I.5. Measures on Compact Metric Spaces

221

(2)

I.6. Topological Groups

223

(1)

Appendix II: On the Foundations of Probability

224

(21)

II.1 Four Different Methods for Investigating Probabilities

224

(8)

II.2. Subjectivist Foundations of Probability

232

(2)

II.3. Subjectivism as an Eliminativist Methodology

234

(3)

II.4. Subjectivist Formulations of Statistical Concepts

237

(3)

II.5. Statistical Explanation

240

(5)

Appendix III: Probability in Nonequilibrium Statistical Mechanics

245

(14)

III.1. Is the Probabilistic Framework of Equilibrium SM too Restrictive?

245

(1)

III.2. Introduction of Probabilities into the SM of Closed Systems

246

(1)

III.3. Systems that Are in a State of Equilibrium with Respect to Their Surroundings

247

(2)

III.4. Formulation of the Framework of NESM

249

(4)

III.5. A Characterization of Mixing

253

(4)

III.6. A Conclusion

257

(2)

Note Added in Proof

258

(1)

Author Index

259

(3)

Subject Index

262

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The Concept of Probability in Statistical Physics

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