Statistical Mechanical Equilibrium| Statistical Mechanical Equilibrium |
In General
> s.a. ergodic theory; fluctuations; states;
thermodynamics; wigner functions.
* 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.
* Calculations:
All quantities of interest can be obtained from the distribution
function; The easiest one to use is the canonical one.
@ Notions of equilibrium: Lavis SHPMP(05);
Pitowsky SHPMP(06);
Lavis PhSc(08)dec
[degrees of equilibrium, incorporating the Boltzmann and Gibbs approaches];
Werndl & Frigg SHPMP(15)-a1510,
a1510 [new definition of equilibrium, and results];
Werndl & Frigg a1606-in
[general criteria for the existence of an equilibrium state],
a1607-proc [with stochastic microdynamics];
Lazarovici a1809 [comment on Werndl & Frigg];
Limaa et al PRD-a1911 [in general relativity].
@ Notions of equilibrium, quantum systems: Bogdanov et al qp/06-conf [as an effect of quantum entanglement];
del Rio et al PRE(16)-a1401 [thermalization relative to a particular reference].
Approach to Equilibrium / Thermalization
> s.a. history of physics.
* Approach to thermal equilibrium:
The circumstances under which a system reaches thermal equilibrium, and how
to derive this from basic dynamical laws, has been a major question from
the very beginning of thermodynamics and statistical mechanics; Some results
are known, such as the correlation between relaxation to equilibrium and chaos
(Krylov showed that a sufficient condition is that the system be mixing), but
it remains an open problem.
* 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.
@ History:
Goldstein LNP-cm/01 [Boltzmann's analysis];
Leeds PhSc(03)jan [Albert's vs Boltzmann's approach].
@ Approach to equilibrium: Lebowitz RMP(99)mp/00;
Flores-Hidalgo et al PRA(09)-a0903 [renormalized-coordinate approach];
Reimann & Evstigneev PRE(13)-a1311 [under experimentally realistic conditions];
Malabarba et al PRE(16)-a1604,
Dong et al a1706 [classical vs quantum equilibration];
Ho & De Roeck a2011 [prethermalization, theory];
> s.a. arrow of time;
diffusion; H-Theorem;
Langevin Equation; thermodynamics [foundations].
@ And ergodicity and chaos: Srednicki PRE(94)cm,
NYAS(95)cm/94,
cm/94 [chaos];
Earman & Rédei BJPS(96) [and ergodic theory];
Gallavotti Chaos(98),
cm/06 [rev; ensembles, ergodicity and chaoticity];
Vranas PhSc(98)dec [generalized, "epsilon" ergodicity];
Zaslavsky PT(99)aug
[limitations of chaotic dynamics, relaxation to equilibrium and decay of fluctuations];
Srednicki JPA(99)cm [quantum chaotic system];
Castiglione et al 08 [and dynamical systems].
@ Microcanonical equilibrium: Bander cm/96;
Hari Dass et al IJMPA(03)cm/01.
@ Related topics: Batterman PhSc(98)jun [Khinchin's program];
Wang et al AJP(07)may [equilibrium with few particles];
Akhmedov a2105 [in an expanding spacetime, equilibration];
> s.a. Maxwell-Boltzmann Distribution;
Thermodynamic Limit.
Thermalization of a Quantum System > s.a. quantum statistical
mechanics; states in quantum statistical mechanics.
* Idea: The first approach was von Neumann's
"quantum ergodic hypothesis"; 2020, a common approach is based on understanding
the spreading of entanglement in out-of-equilibrium quantum many-body systems; Other
approaches are based on the eigenstate thermalization hypothesis and on entropy production;
One can get mixed states from pure states by coarse-graining, or some self-thermalization.
@ General references: Albert BJPS(94) [and the collapse of a quantum wave function];
Hari Dass et al IJMPA(03)cm/01 [self-thermalization];
Scarani EPJST(07)-a0707 [entanglement and irreversibility];
Reimann PRL(08), comment
Gong & Duan a1109 [realistic quantum system];
Linden et al PRE(09)-a0812;
Lychkovskiy PRE(10)-a0903;
Yuan et al JPSJ(09)-a0904 [decoherence and thermalization];
Cho & Kim PRL(10)-a0911 [from pure quantum states];
Yuan et al JPSJ(09)-a0904 [decoherence and thermalization];
Cho & Kim PRL(10)-a0911 [from pure quantum states];
Tasaki a1003 [proof and examples];
Ponomarev et al PRL(11)-a1004;
Dizadji-Bahmani PhSc(11) [Aharonov approach];
Riera et al PRL(12)-a1102 [in nature and on a quantum computer];
Ponomarev et al EPL(12)-a1107 [between two finite systems, from equipartition];
Cui et al a1110;
Cramer NJP(12)-a1112 [randomized local Hamiltonians];
Larson JPB(13)-a1304 [and non-integrability];
Yang et al PRE(14)-a1311 [canonical vs non-canonical equilibration dynamics];
Xiong et al SRep(15)-a1311 [and non-Markovian dynamics];
Khlebnikov & Kruczenski a1312 [isolated system];
Gogolin & Eisert RPP(16)-a1503 [rev];
Ithier & Benaych-Georges a1510 [from first principles],
PRA(17)-a1706 [and random interactions];
Zhdanov et al PRL(17)-a1706 [not without correlations];
Grimmer et al a1805;
Dymarsky a1806 [isolated system];
Parker et al PRX(19);
Koukoulekidis et al a1912
[emergence of the Gibbs state from passive states];
Jacob et al a2012 [from quantum scattering].
@ Eigenstate Thermalization Hypothesis:
Rigol & Srednicki PRL(12) [alternatives];
De Palma et al PRL(15)-a1506;
Hosur & Qi PRE(16)-a1507;
D'Alessio et al AiP(16)-a1509 [and consequences];
Deutsch RPP(18) [rev];
Richter et al PRE(19)-a1805 [and the route to equilibrium];
Foini & Kurchan PRE(19)-a1809 [and out-of-time-order correlators];
Inozemcev & Volovich a1811 [modified formulation];
Campos Venuti & Liu a1904 [and quantum ergodicity];
Wilming et al PRL(19);
Inozemcev & Volovich a2002 [and thermalization];
Sugimoto et al a2005 [test].
@ Entropy production:
Esposito et al NJP(10);
Ptaszyński & Esposito PRL(19) [open system].
@ Time scales: Brandão et al PRE(12)-a1108 [under a random Hamiltonian];
Short & Farrelly NJP(12)-a1110 [bound];
Goldstein et al PRL(13)-a1307,
NJP(15)-a1402;
García-Pintos et al PRX(17)-a1509;
Farrelly NJP(16)-a1512.
@ Macroscopic, many-body systems: Goldstein et al PRE(10)-a0911;
Reimann NJP(10);
Torres-Herrera et al PS(15)-a1403 [many-body systems, numerical and analytical studies];
Tasaki JSP(16)-a1507 [isolated, and typicality];
Ostilli & Presilla PRA(17)-a1611 [phenomenological theory];
Swingle & Yao Phy(17) scrambling of information in spin systems];
Anza a1808-PhD [and quantum gravity];
> s.a. Superpositions.
@ Other types of systems: Belton CMP(10) [quantum random walks];
Kota et al JSM(11)-a1102 [two-body random ensemble];
Veniaminov a1112 [interacting particles in a random medium];
Blanc & Lewin JMP(12)-a1201 [disordered quantum Coulomb systems];
Kay a1209
[system and bath of comparable sizes, and black holes];
Sedlmayr et al PRL(13)-a1212 [1D fermionic chain];
Zhuang & Wu PRE(13)-a1308 [chaotic system];
Campbell et al SRep(16)-a1507 [bosonic atoms in a double-well potential];
Cherian et al EPL(19)-1604 [two-level quantum system];
Tang et al PRX(18) [dipolar quantum Newton's cradle];
Jaschke et al a1805 [1D Ising chain];
Gluza et al a1809 [non-interacting lattice fermions];
van Enk a1810 [two identical bosons];
Wang et al a1905 [small quantum systems].
Examples of Systems
@ General references: Rothstein AJP(57)nov [irreversibility and information in nuclear spin echo];
Nauenberg AJP(04)mar [radiation].
@ Breakdown of thermalization:
news pw(06)apr [gas that does not approach equilibrium];
Rigol PRL(09) [and integrability];
Wang et al EPJD(13)-a1207 [non-Markovian dynamics in a spin star system].
main page
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send feedback and suggestions to bombelli at olemiss.edu – modified 11 may 2021