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

by Lawrence Sklar

• ISBN13: 9780521558815
• ISBN10: 0521558816
• Format: Paperback
• Copyright: 1995-09-29
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Preface	xiii
Introduction	1	(13)
Philosophy and the foundations of physics	1	(6)
The structure of this book	7	(4)
Probability	7	(1)
Statistical explanation	8	(1)
The equilibrium problem	9	(1)
The non-equilibrium problem	9	(1)
Cosmology and statistical mechanics	10	(1)
The reduction of thermodynamics to statistical mechanics	10	(1)
The direction of time	11	(1)
Notes to the reader	11	(3)
Historical sketch	14	(76)
Thermodynamics	15	(13)
Phenomenological properties and laws	15	(1)
Conservation and irreversibility	16	(4)
Formal thermostatics	20	(2)
Extending thermodynamics	22	(6)
Kinetic theory	28	(20)
Early kinetic theory	28	(2)
Maxwell	30	(2)
Boltzmann	32	(2)
Objections to kinetic theory	34	(3)
The probabilistic interpretation of the theory	37	(7)
The origins of the ensemble approach and of ergodic theory	44	(4)
Gibbs' statistical mechanics	48	(11)
Gibbs' ensemble approach	48	(3)
The thermodynamic analogies	51	(2)
The theory of non-equilibrium ensembles	53	(6)
The critical exposition of the theory of P. and T. Ehrenfest	59	(12)
The Ehrenfests on the Boltzmannian theory	60	(7)
The Ehrenfests on Gibbs' statistical mechanics	67	(4)
Subsequent developments	71	(17)
The theory of equilibrium	71	(5)
Rationalizing the equilibrium theory	76	(5)
The theory of non-equilibrium	81	(5)
Rationalizing the non-equilibrium theory	86	(2)
Further readings	88	(2)
Probability	90	(38)
Formal aspects of probability	91	(5)
The basic postulates	91	(2)
Some consequences of the basic postulates and definitions	93	(2)
Some formal aspects of probability in statistical mechanics	95	(1)
Interpretations of probability	96	(24)
Frequency, proportion, and the ``long run''	97	(2)
Probability as a disposition	99	(3)
``Probability'' as a theoretical term	102	(6)
Objective randomness	108	(2)
Subjectivist accounts of probability	110	(7)
Logical theories of probability	117	(3)
Probability in statistical mechanics	120	(7)
Further readings	127	(1)
Statistical explanation	128	(28)
Philosophers on explanation	128	(20)
Causation and the Humean critique	128	(3)
Explanation as subsumption under generality	131	(9)
Subsumption, causation and mechanism, and explanation	140	(8)
Statistical explanation in statistical mechanics	148	(6)
Further readings	154	(2)
Equilibrium theory	156	(40)
Autonomous equilibrium theory and its rationalization	156	(8)
From Maxwell's equilibrium distribution to the generalized micro-canonical ensemble	156	(3)
The Ergodic Hypothesis and its critique	159	(3)
Khinchin's contribution	162	(2)
The development of contemporary ergodic theory	164	(11)
The results of von Neumann and Birkhoff	164	(3)
Sufficient conditions for ergodicity	167	(2)
The KAM Theorem and the limits of ergodicity	169	(6)
Ergodicity and the rationalization of equilibrium statistical mechanics	175	(19)
Ensemble probabilities, time probabilities, and measured quantities	176	(3)
The uniqueness of the invariant probability measure	179	(3)
The set of measure zero problem	182	(6)
Ergodicity and equilibrium theory in the broader non-equilibrium context	188	(2)
The objective Bayesian approach to equilibrium theory	190	(4)
Further readings	194	(2)
Describing non-equilibrium	196	(23)
The aims of the non-equilibrium theory	196	(3)
General features of the ensemble approach	199	(8)
Non-equilibrium theory as the dynamics of ensembles	199	(3)
Initial ensembles and dynamical laws	202	(5)
Approaches to the derivation of kinetic behavior	207	(8)
The kinetic theory approach	207	(3)
The master equation approach	210	(2)
The approach using coarse-graining and a Markov process assumption	212	(3)
General features of the rationalization program for the non-equilibrium theory	215	(2)
Further readings	217	(2)
Rationalizing non-equilibrium theory	219	(78)
Two preliminaries	219	(5)
The spin-echo experiments	219	(3)
Computer modeling of dynamical systems	222	(2)
Rationalizing three approaches to the kinetic equation	224	(22)
The rigorous derivation of the Boltzmann equation	224	(4)
The generalized master equation	228	(4)
Beyond ergodicity	232	(10)
Representations obtained by non-unitary transformations	242	(2)
Macroscopic chaos	244	(2)
Interpretations of irreversibility	246	(33)
Time-asymmetric dynamical laws	246	(4)
Interventionist approaches	250	(5)
Jaynes' subjective probability approach	255	(5)
The mainstream approach to irreversibility and its fundamental problems	260	(2)
Krylov's program	262	(7)
Prigogine's invocation of singular distributions for intial ensembles	269	(8)
Confliciting rationalizations	277	(2)
The statistical explanation of non-equilibrium behavior	279	(16)
Probabilities as features of collections of systems	281	(7)
Probabilities as features of states of individual systems	288	(5)
Initial conditions and symmetry-breaking	293	(2)
Further readings	295	(2)
Cosmology and irreversibility	297	(36)
The invocation of cosmological considerations	297	(10)
Boltzmann's cosmological way out	297	(3)
Big Bang cosmologies	300	(3)
Expansion and entropy	303	(2)
Radiation asymmetry and cosmology	305	(2)
Conditions at the initial singularity	307	(11)
Initial low entropy	307	(2)
Accounting for the initial low entropy state	309	(9)
Branch systems	318	(13)
The idea of branch systems	318	(1)
What cosmology and branch systems can't do	319	(12)
Further readings	331	(2)
The reduction of thermodynamics to statistical mechanics	333	(42)
Philosophical models of inter-theoretic reduction	333	(12)
Positivist versus derivational models of reduction	333	(4)
Concept bridging and identification	337	(4)
The problem of radically autonomous concepts	341	(4)
The case of thermodynamics and statistical mechanics	345	(16)
The special nature of the reduced and reducing theories	345	(3)
Connecting the concepts of the two theories	348	(13)
Problematic aspects of the reduction	361	(12)
Conservative versus radical ontological approaches	361	(6)
The emergence of thermal features	367	(6)
Further readings	373	(2)
The direction of time	375	(38)
The Boltzmann thesis	375	(3)
Asymmetry of time or asymmetries in time?	378	(7)
Symmetries of laws and symmetries of space-time	379	(3)
Entropic asymmetry and the asymmetry of time	382	(3)
What is the structure of the Boltzmann thesis?	385	(26)
The intuitive asymmetries	385	(2)
What is the nature of the proposed entropic theory of the intuitive asymmetries?	387	(9)
Sketches of some entropic accounts	396	(8)
Our inner awarencess of time order	404	(7)
Further readings	411	(2)
The current state of the major questions	413	(8)
References	421	(8)
Index	429