Time, Chance, and Reduction: Philosophical Aspects of Statistical Mechanics

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Contributors......Page 8
1.1 Statistical mechanics and philosophy......Page 9
1.2 The arrows of time......Page 11
1.3 Probability and chance......Page 13
1.4 Reduction......Page 15
References......Page 17
Part I The arrows of time......Page 19
2.1 Introduction......Page 21
2.2 The micro-statistical account......Page 23
2.3 Trees or webs......Page 24
2.4 Causal handles......Page 34
2.5 Decision counterfactuals......Page 36
References......Page 40
3.1 Introduction......Page 42
3.2 The past hypothesis......Page 45
3.3 The past hypothesis meets gravity......Page 48
3.4 The gravitational paradoxes......Page 50
3.5 The problem......Page 55
3.6 A way forward?......Page 59
References......Page 64
4.1 Arrows of time......Page 67
4.2 Quantum gravity......Page 71
4.3 Low-entropy condition from quantum gravity......Page 74
References......Page 75
Part II Probability and chance......Page 77
5.1 Objective interpretations of probability......Page 79
5.2 From the classical interpretation to the range interpretation......Page 81
5.3 The natural-range interpretation of probability......Page 83
5.4 The method of arbitrary functions......Page 91
5.5 The main objection to the range interpretation......Page 94
References......Page 98
6.2 Boltzmannian statistical mechanics......Page 100
6.3.1 Introducing macro-probabilities......Page 103
6.3.2 Macro-probabilities scrutinized......Page 105
6.4.1 Introducing micro-probabilities......Page 108
6.4.2 Humean chance......Page 110
6.4.3 Problems with fit......Page 113
6.4.4 The putative best system is not the best system......Page 117
6.4.5 Interpreting BSM probabilities......Page 122
6.5 Conclusion......Page 124
References......Page 125
7.1 Humean metaphysics......Page 127
7.2 Causal properties......Page 132
7.3 The master argument against Humeanism and the ontology of science......Page 136
References......Page 141
Part III Reduction......Page 145
8.2 The essentials of the structuralist representation of theories......Page 147
8.3 The historical data......Page 150
8.4 The basic theory-element of Cl-1......Page 151
8.5 The specializations of Cl-1......Page 156
8.6 The basic theory-element of Clausius-2.1......Page 158
8.7 Specializations of Cl-2.1......Page 160
8.8 The basic theory-element of Clausius-2.2......Page 161
8.9 Specializations......Page 163
References......Page 165
9.1 Introduction......Page 167
9.2 Philosophical reduction......Page 168
9.3 Gibbs\' caution and the \'non-equivalence’ of ensembles......Page 170
9.5 The micro-canonical ensemble......Page 172
9.6 Limiting reductions/limiting relations between theories......Page 173
9.7 The renormalization group, the central limit theorem, and the equivalence of ensembles......Page 175
9.8 Critical phenomena: the inequivalence of ensembles......Page 183
9.9 Conclusion......Page 186
References......Page 187
10.1 Introduction......Page 188
10.2 The definition of Markov processes......Page 191
10.3 Stochastic dynamics......Page 194
10.4 Approach to equilibrium and increase of entropy?......Page 197
Ad (ii)......Page 199
Ad (iv)......Page 201
10.5.1 Coarse graining and the repeated randomness assumption......Page 202
10.5.2 Interventionism or \'open systems’......Page 205
Ad (v)......Page 208
10.7 Reversibility of stochastic processes......Page 212
References......Page 213
Index......Page 216