Cover

Physics and chance

Title

Copyright

Dedication

Contents

Preface

1. Introduction

I. Philosophy and the foundations of physics

II. The structure of this book

1. Probability

2. Statistical explanation

3. The equilibrium problem

4. The non-equilibrium problem

5. Cosmology and statistical mechanics

6. The reduction of thermodynamics to statistical mechanics

7. The direction of time

III. Notes to the reader

2. Historical sketch

I. Thermodynamics

1. Phenomenological properties and laws

2. Conservation and irreversibility

3. Formal thermostatics

4. Extending thermodynamics

ll. Kinetic theory

1. Early kinetic theory

2. Maxwell

3. Boltzmann

4. Objections to kinetic theory

5. The probabilistic interpretation of the theory

6. The origins of the ensemble approach and of ergodic theory

III. Gibbs' statistical mechanics

1. Gibbs' ensemble approach

2. The thennodynamic analogies

3. The theory of non-equilibrium ensembles

IV. The critical exposition of the theory of P. and T. Ehrenfest

1. The Ehrenfests on the Boltzmannian theory

2. The Ehrenfests on Gibbs' statistical mechanics

V. Subsequent developments

1. The theory of equilibrium

2. Rationalizing the equilibrium theory

3. The theory of non-equilibrium

4. Rationalizing the non-equilibrium theory

VI. Further readings

3. Probability

I. Formal aspects of probability

1. The basic postulates

2. Some consequences of the basic postulates and definitions

3. Some formal aspects of probability in statistical mechanics

ll. Interpretations of probability

1. Frequency, proportion, and the "long run"

2. Probability as a disposition

3. ''Probability'' as a theoretical term

4. Objective randomness

5. Subjectivist accounts of probability

6. Logical theories of probability

III. Probability in statistical mechanics

IV. Further readings

4. Statistical explanation

I. Philosophers on explanation

1. Causation and the Humean critique

2. Explanation as subsumption under generality

3. Subsumption, causation and mechanism, and explanation

ll. Statistical explanation in statistical mechanics

Ill. Further readings

5. Equilibrium theory

I. Autonomous equilibrium theory and its rationalization

1. From Maxwell's equilibrium distribution to the generalized micro-canonical ensemble

2. The Ergodic Hypothesis and its critique

3. Khinchin's contribution

II. The Development of contemporary ergodic theory

1. The results of von Neumann and Birkhoff

2. Sufficient conditions for ergodicity

3. The KAM Theorem and the limits of ergodicity

III. Ergodicity and the rationalization of equilibrium statistical mechanics

1. Ensemble probabilities, time probabilities, and measured quantities

2. The uniqueness of the invariant probability measure

3. The set of measure zero problem

4. Ergodicity and equilibrium theory in the broader non-equilibrium context

5. The Objective Bayesian approach to equilibrium theory

IV. Further readings

6. Describing non-equilibrium

I. The aims of the non-equilibrium theory

II. General features of the ensemble approach

1. Non-equilibrium theory as the dynamics of ensembles

2. Initial ensembles and dynamical laws

III. Approaches to the derivation of kinetic behavior

1. The kinetic theory approach

2. The master equation approach

3. Tbe approach using coarse-graining and a Markov process assumption

IV. General features of the rationalization program for the non-equilibrium theory

V. Further readings

7. Rationalizing non-equilibrium theory

I. Two prellminarles

1. The spin-ecbo experiments

2. Computer modeling of dynamical systems

II. Rationalizing three approaches to the kinetic equation

1. The rigorous derivation of the Boltzmann equation

2. The generalized master equation

3. Beyond ergodicity

4. Representations obtained by non-unitary transformations

5. Macroscopic chaos

III. Interpretations of irreversibility

1. Time-asymmetric dynamical laws

2. Interventionist approaches

3. Jaynes' subjective probability approach

4. The mainstream approach to irreversibility and its fundamental problems

5. Krylov's program

6. Prigogine's invocation of Singular distributions for initial ensembles

7. Conflicting rationalizations

IV. The statistical explanation of non-equllibrium behavior

1. Probabilities as features of collections of systems

2. Probabilities as features of states of individual systems

3. Initial conditions and symmetry-breaking

V. Further readings

8. Cosmology and irreversibility

I. The invocation of cosmological considerations

1. Boltzmann's cosmological way out

2. Big Bang cosmologies

3. Expansion and entropy

4. Radiation asymmetry and cosmology

ll. Conditions at the initial singularity

1. Initial low entropy

2. Accounting for the initial low-entropy state

III. Branch systems

1. The idea of branch systems

2. What cosmology and branch systems can't do

IV. Further readings

9. The reduction of thermodynamics to statistical mechanics

I. Philosophical models of intertheoretic reduction

1. Positivist versus derivational models of reduction

2. Concept-bridging and identification

3. The problem of radically autonomous concepts

ll. The case of thermodynamics and statistical mechanics

1. The special nature of reduced and reducing theories

2. Connecting the concepts of the two theories

III. Problematic aspects of the reduction

1. Conservative versus radical ontological approaches

2. The emergence of thermal features

IV. Further readings

10. The direction of time

I. The Boltzmann thesis

ll. Asymmetry of time or asymmetries in time?

1. Symmetries of laws and symmetries of space-time

2. Entropic asymmetry and the asymmetry of time

III. What is the structure of the Boltzmann thesis?

1. The intuitive asymmetries

2. What is the nature of the proposed entropic theory of the intuitive asymmetries?

3. Sketches of some entropic accounts

4. Our inner awareness of time order

IV. Further readings

11. The current state of major questions

References

Index