Physics and Chance: Philosophical Issues in the Foundations of Statistical Mechanics

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Cambridge University Press, Sep 29, 1995 - Philosophy - 437 pages
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Statistical mechanics is one of the crucial fundamental theories of physics, and in his new book Lawrence Sklar, one of the pre-eminent philosophers of physics, offers a comprehensive, non-technical introduction to that theory and to attempts to understand its foundational elements. Among the topics treated in detail are: probability and statistical explanation, the basic issues in both equilibrium and non-equilibrium statistical mechanics, the role of cosmology, the reduction of thermodynamics to statistical mechanics, and the alleged foundation of the very notion of time asymmetry in the entropic asymmetry of systems in time. The book emphasises the interaction of scientific and philosophical modes of reasoning, and in this way will interest all philosophers of science as well as those in physics and chemistry concerned with philosophical questions. The book could also be read by an informed general reader interested in the foundations of modern science.
  

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Contents

Introduction
1
II The structure of this book
7
2 Statistical explanation
8
3 The equilibrium problem
9
5 Cosmology and statistical mechanics
10
7 The direction of time
11
Historical sketch
14
I Thermodynamics
15
IV Further readings
194
Describing nonequilibrium
196
II General features of the ensemble approach
199
2 Initial ensembles and dynamical laws
202
III Approaches to the derivation of kinetic behavior
207
2 The master equation approach
210
3 The approach using coarsegraining and a Markov process assumption
212
IV General features of the rationalization program for the nonequilibrium theory
215

2 Conservation and irreversibility
16
3 Formal thermostatics
20
4 Extending thermodynamics
22
II Kinetic theory
28
2 Maxwell
30
3 Boltzmann
32
4 Objections to kinetic theory
34
5 The probabilistic interpretation of the theory
37
6 The origins of the ensemble approach and of ergodic theory
44
III Gibbs statistical mechanics
48
2 The thermodynamic analogies
51
3 The theory of nonequilibrium ensembles
53
IV The critical exposition of the theory of P and T Ehrenfest
59
1 The Ehrenfests on the Boltzmannian theory
60
2 The Ehrenfests on Gibbs statistical mechanics
67
V Subsequent developments
71
2 Rationalizing the equilibrium theory
76
3 The theory of nonequilibrium
81
4 Rationalizing the nonequilibrium theory
86
VI Further readings
88
Probability
90
I Formal aspects of probability
91
2 Some consequences of the basic postulates and definitions
93
3 Some formal aspects of probability in statistical mechanics
95
II Interpretations of probability
96
1 Frequency proportion and the long run
97
2 Probability as a disposition
99
3 Probability as a theoretical term
102
4 Objective randomness
108
5 Subjectivist accounts of probability
110
6 Logical theories of probability
117
III Probability in statistical mechanics
120
IV Further readings
127
Statistical explanation
128
2 Explanation as subsumption under generality
131
3 Subsumption causation and mechanism and explanation
140
II Statistical explanation in statistical mechanics
148
III Further readings
154
Equilibrium theory
156
2 The Ergodic Hypothesis and its critique
159
3 Khinchins contribution
162
II The Development of contemporary ergodic theory
164
2 Sufficient conditions for ergodicity
167
3 The KAM Theorem and the limits of ergodicity
169
III Ergodicity and the rationalization of equilibrium statistical mechanics
175
1 Ensemble probabilities time probabilities and measured quantities
176
2 The uniqueness of the invariant probability measure
179
3 The set of measure zero problem
182
4 Ergodicity and equilibrium theory in the broader nonequilibrium context
188
5 The Objective Bayesian approach to equilibrium theory
190
V Further readings
217
Rationalizing nonequilibrium theory
219
2 Computer modeling of dynamical systems
222
II Rationalizing three approaches to the kinetic equation
224
2 The generalized master equation
228
3 Beyond ergodicity
232
4 Representations obtained by nonunitary transformations
242
5 Macroscopic chaos
244
III Interpretations of irreversibility
246
2 Interventionist approaches
250
3 Jaynes subjective probability approach
255
4 The mainstream approach to irreversibility and its fundamental problems
260
5 Krylovs program
262
6 Prigogines invocation of singular distributions for initial ensembles
269
7 Conflicting rationalizations
277
IV The statistical explanation of nonequilibrium behavior
279
1 Probabilities as features of collections of systems
281
2 Probabilities as features of states of individual systems
288
3 Initial conditions and symmetrybreaking
293
V Further readings
295
Cosmology and irreversibility
297
2 Big Bang cosmologies
300
3 Expansion and entropy
303
4 Radiation asymmetry and cosmology
305
II Conditions at the initial singularity
307
2 Accounting for the initial lowentropy state
309
III Branch systems
318
2 What cosmology and branch systems cant do
319
IV Further readings
331
The reduction of thermodynamics to statistical mechanics
333
2 Conceptbridging and identification
337
3 The problem of radically autonomous concepts
341
II The case of thermodynamics and statistical mechanics
345
2 Connecting the concepts of the two theories
348
III Problematic aspects of the reduction
361
2 The emergence of thermal features
367
IV Further readings
373
The direction of time
375
II Asymmetry of time or asymmetries in time?
378
1 Symmetries of laws and symmetries of spacetime
379
2 Entropic asymmetry and the asymmetry of time
382
III What is the structure of the Boltzmann thesis?
385
2 What is the nature of the proposed entropic theory of the intuitive asymmetries?
387
3 Sketches of some entropic accounts
396
4 Our inner awareness of time order
404
IV Further readings
411
The current state of major questions
413
References
421
Index
429
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Page 440 - is the James B. and Grace J. Nelson Professor of Philosophy at the University of Michigan. He is the author of Space, Time, and Spacetime

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About the author (1995)

Lawrence Sklar is the Carl G. Hempel and William K. Frankena Distinguished University Professor at the University of Michigan. He is the author of Space, Time and Spacetime (1992), Philosophy of Physics (1992), Physics of Chance (Cambridge University Press, 1995) and Theory and Truth (2000).

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