Statistical
Mechanics| Statistical
Mechanics |
In General > s.a. non-equilibrium;
quantum statistical mechanics; stochastic
processes; 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.
@ Foundations: Rothstein AJP(51)
[and nuclear spin echo]; Penrose RPP(79);
Albert BJPS(94);
Zaslavsky PT(99)aug; Sklar BJPS(00);
Goldstein cm/01-in
[Boltzmann];
Gross PCCP(02)cm [geometric];
Leeds PhSc(03)jan
[Albert's vs Boltzmann's approach]; Gallavotti
Chaos(98), cm/06 [rev;
ensembles, ergodicity and chaoticity].
@ Thermodynamic limit: Compagner AJP(89) [continuum limit]; Styer AJP(04)
[paradoxes]; Batterman SHPMP(05)
[validity of idealized limit].
@ Related topics: Aizenman mp/06.
Equilibrium Statistical Mechanics > s.a. ergodic
theory; fluctuations; states
in statitsical mechanics; wigner functions.
* Calculations: All quantities
of interest can be obtained from the distribution
function; The easiest one to use is the canonical one.
* Approaches: Statistical
mechanics attempts to situate equilibrium at the macroscopic level in the Boltzmann
approach
and at the statistical level in the Gibbs approach; The issue has not really
been settled.
* Remark: The distribution
function in some phenomena, such as very unstable systems like K-flows,
appears to be fundamental, and not just a way of encoding our ignorance.
@ Approach to equilibrium: Srednicki PRE(94)cm,
cm/94-in,
cm/94 [and
chaos]; Bander cm/96 [microcanonical];
Srednicki JPA(99)cm [quantum
chaotic system]; Lebowitz RMP(99)mp/00;
Nauenberg AJP(04)
[radiation]; Lavis SHPMP(05)
[notion of equilibrium]; > s.a. arrow of
time, H-Theorem, quantum
statistical mechanics,
thermodynamics [foundations].
@ Related topics: Batterman PhSc(98),
Vranas PhSc(98)
[reasons]; news pw(06)apr
[gas
that does not approach equilibrium]; Bogdanov et al qp/06-in
[equilibrium as
quantum
entanglement]; Pitowsky SHPMP(06)
[def of equilibrium]; Wang et al AJP(07)
[equilibrium with few particles].
Specific Aspects and Techniques > s.a. critical
phenomena;
entropy; models [including non-extensive]; phase
space; Transport.
@ 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).
@ And dynamical systems: Ruelle & Sinai PhyA(86); McCoy mp/99-in
[integrable models].
@ 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 H's]; Fernández AJP(03),
Decoster JPA(04)
[perturbation theory];
Emch SHPMP(05)
[probabilistic issues]; > s.a. Gibbs Paradox,
Instabilities, Liouville
Theorem, Mean Field, Pressure, Scaling, Spin
Echo.
References > s.a. history
of physics;
physics teaching; thermodynamics and
modified thermodynamics [including relativistic].
@ Books: Jancovici ed-66 [Cargèse lectures]; O 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; Martynov
97; Chowdhury & Stauffer 00; Mazenko
00; Guénault 07.
@ Texts, II: Kittel 58; Morse 64; Kubo et al 65; Reif 65 [II-III];
Kittel & Kroemer 80; Mandl 88; Gasser & Richards
95; Amit & Verbin 99; Baierlein 99; Bowley & Sánchez
99; Dorlas 99 [& III]; Schroeder 00; Glazer & Wark 01;
Blundell & Blundell 06 [r PT(07)oct];
Mattis & Swendsen 08 [& III].
@ Texts,
III:
Huang 87; Pathria 96; Reichl 98;
Gallavotti 99; Kadanoff 00; Phillies 00; Salinas 01; Honerkamp 02; Le Bellac
et al 04; Cowan 05;
Plischke & Bergersen 06 [includes
critical phenomena]; Schwabl 06 [includes non-equilibrium]; Sachs
et al 06; Kardar 07, 07 [particles + fields]; Van Vliet 08 [includes non-equilibrium].
@ Texts, chemistry emphasis: Hill 87; Chandler 87; McQuarrie 00.
@ Texts, condensed matter emphasis: Goodstein 85; Hermann
05.
@ Texts, other emphasis: Sklar 94 [conceptual]; Tanaka
02 [cluster variation method]; Sethna 06 [entropy, complexity, r PT(07)may].
@ Texts, problems: Lim 90;
Dalvit et al 99.
@ Texts, algebraic: Emch 72;
Kastler ed-76; Bratteli & Robinson 81, 87.
@ Texts, classical: Khinchin 49; Ruelle 69; Thompson 88; Robertson 93.
@ Texts, geometrical: Morandi et al 01 [dg, foundations];
Brody & Hughston 03 [geometry].
@ Texts, probability: Mayants 84; Guttmann 99.
Online Resources > see Wikibooks main page; SklogWiki main page.
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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Send feedback and suggestions to bombelli at olemiss.edu – Modified
21 jun 2008