Statistical Mechanics  

In General > s.a. equilibrium; non-equilibrium systems; quantum statistical mechanics; thermodynamics.
* Levels of description: For a system of many particles there are three, microscopic/dynamic (described by particle mechanics), macroscopic/statistical, and thermodynamic; Statistical mechanics describes the middle level, using probability distributions to treat fluctuations and probabilities of various configurations.
* Motivation for statistical description: Ignorance of microscopic degrees of freedom, effect of the environment that over the time of a measurement causes the system to fluctuate, and ergodic-type arguments according to which even an isolated system will explore a large part of the available phase space over measurement-type time scales.
* Foundational problem: Physically, what we know or don't know about a system can't affect its evolution, but in a statistical mechanics interpretation of thermodynamics the information is crucial in explaining the evolution towards equilibrium.
@ General references, foundations: Penrose RPP(79); Gross PCCP(02)cm [geometric]; Aizenman in(07)mp/06; Singh a1103-RMP [how and why it works]; > s.a. equilibrium [thermalization].

Specific Aspects and Techniques > s.a. non-extensive statistics; phase space; statistical mechanical systems; Thermodynamic Limit.
@ Path-integral methods: Wiegel PRP(75); Abrikosov NPB(92); Chaichian & Demichev 01.
@ Large deviations: Donsker & Varadhan PRP(81); Strook 84; Ellis 85; Lebowitz et al JMP(00); Touchette PRP(09), a1106-ln; Ruiz & Tsallis a1110.
@ Probabilistic issues: Emch SHPMP(05); Winsberg SHPMP(08) [interpretation]; Frigg PhSc(08)dec [as chances in David Lewis' sense]; Swendsen AJP(14)oct [unnormalized probabilities].
@ Geometric: Brody & Hughston PRS(99)gq/97 [projective geometry]; Casetti et al PRP(00); Portesi et al PhyA(07) [generalized].
@ Related topics: Ercolessi et al IJMPA(02)qp/01 [use of different Hs]; Fernández AJP(03)nov, Decoster JPA(04) [perturbation theory]; Velazquez Abad AP(12) [and complementarity]; Majewski & Labuschagne AHP(14)-a1302 [rigorous approach based on Orlicz spaces].
>
Phenomena and systems: see critical phenomena; Gibbs Paradox; Polymers [polymer expansion]; Spin Echo; Transport.
> Concepts and results: see entropy; Instabilities; Liouville Theorem; Orlicz Space; Paradoxes; Pressure; Scaling; stochastic processes; Tropical Limit.
> Techniques: see analysis [fractional]; computational physics; Mean-Field Theory; renormalization group; Transfer-Matrix Method.

References > s.a. history of physics; physics teaching; thermodynamics and modified thermodynamics [including relativistic].
@ Texts: Jancovici ed-66 [Cargèse lectures]; Penrose 70; Ishihara 71; Feynman 72; Landsberg 79; Tolman 79; Landau & Lifshitz 80; Lifshitz & Pitaevskii 80; Vasilyev 84; Ma 85; Klimontovich 86; Grandy 87; Agarwal & Eisner 88; Balian 91; Bogoliubov 91; Lavenda 91; Toda et al 92; Greiner et al 95; Chowdhury & Stauffer 00; Mazenko 00; Guénault 07.
@ Texts, II: Kittel 58; Morse 64; Kubo et al 65; Reif 65 [II-III]; Kittel & Kroemer 80 [statistical mechanics first]; Mandl 88; Gasser & Richards 95; Amit & Verbin 99; Baierlein 99; Bowley & Sánchez 99; Dorlas 99 [& III]; Schroeder 00; Glazer & Wark 01; Mattis & Swendsen 08 [& III]; Blundell & Blundell 09 [r PT(07)oct]; Helrich 09 [includes irreversibility]; Huang 09; Rudra & Rudra 09; Benguigui 10; Gould & Tobochnik 10; Dalarsson et al 11; Hoch 11; Swendsen 12; Müller-Kirsten 13; Goodstein 15; Olla 15.
@ Texts, III: Minlos RMS(68); Huang 87; Gallavotti 99; Kadanoff 00; Phillies 00; Salinas 01; Honerkamp 02; Le Bellac et al 04; Cowan 05; Plischke & Bergersen 06 [includes critical phenomena]; Halley 06; Schwabl 06 [includes non-equilibrium]; Sachs et al 10; Kardar 07, 07 [particles + fields, r PT(09)may Chandler]; Van Vliet 08 [includes non-equilibrium]; Reichl 09; McCoy 10 [advanced]; Tuckerman 10 [molecular simulations]; Pathria & Beale 11; Peliti 11 [r PT(12)aug]; Walecka 11; Ford 13 [II/III]; in Thorne & Blandford 15.
@ Chemistry emphasis: Hill 87; Chandler 87; McQuarrie 00.
@ Condensed-matter emphasis: Goodstein 85; Hermann 05; Di Castro & Raimondi 15.
@ Problems: Lim 90; Dalvit et al 99.
@ Algebraic: Emch 72; Kastler ed-76; Bratteli & Robinson 81, 87.
@ Classical: Khinchin 49; Ruelle 69; Thompson 88; Robertson 93; Martynov 97.
@ Geometrical: Morandi et al 01 [differential geometry, foundations]; Brody & Hughston 03 [geometry]; Castiglione et al 08 [dynamical systems].
@ Probability: Mayants 84; Guttmann 99.
@ Other emphasis: Sklar 94 [conceptual]; Tanaka 02 [cluster variation method]; Sethna 06 [entropy, complexity, r PT(07)may]; Ernst & Hüttemann ed-10 [philosophical]; Fisher 16 [reviews].

Online Resources > see Wikibooks main page; SklogWiki main page; compadre.org Statistical and Thermal Physics teaching resources.

Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906,
by his own hand. Paul Ehrenfest, carrying on the same work, died similarly in 1933. Now
it is our turn to study statistical mechanics. — D L Goodstein, States of Matter, 1985


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