Non-Equilibrium Statistical Mechanics and Thermodynamics

In General > s.a. quantum field theory; quantum statistical mechanics; statistical mechanics [approach to equilibrium].
* Idea: The study of properties of non-equilibrium states (find special states equivalent to canonical ensembles for equilibrium statistical mechanics; Characterize them in terms of order/chaos, at various scales and near/far from equilibrium), and understand their dynamics (near-equilibrium transport phenomena, the arrow of time, for which we need an irreversible, non-unitary evolution for ).
* History: XIX century, Lord Kelvin; 1931, L Onsager proposed regression equations for evolution of macroscopic variables, in terms of thermodynamic forces; 1953, Onsager & Machlup added white noise; Recently, computer simulations, e.g. using cellular automata (G Jona-Lasinio, C Laudin & M-E Vares).
* Features: Far from equilibrium a system can develop spontaneous ordered structures with specific patterms (but there is no extremum principle to tell us which); This led us not to believe anymore in the "thermal death" of the universe.
* Tools: Intensive thermodynamic parameters can be associated to additive conserved quantities (such as mass, volume, ...) using a statistical approach in far-from-equilibrium steady-state systems, under few assumptions and without a detailed balance requirement.
@ Books, overviews: Balescu 75, 97; Lavenda 85; Keizer 87; Brenig 89; Eu 98; Gaspard 98; Ruelle PhyA(99); Gorban & Karlin cm/03 [geometrical]; Ruelle PT(04)may [rev]; Pokrovski EJP(05); Abou Salem mp/06 [quantum, and thermodyamics]; Ebeling & Sokolov 05; Öttinger 05; Gaspard PhyA(06) [rev]; Maes et al mp/07-ln; Mazenko 07; Evans & Morriss 08 [liquids]; Ódor 08; Streater 09 [stochastic approach].
@ Framework, tools: Schlögl PRP(80) [stochastic measures]; Gaveau & Schulman PLA(97) [master equation]; Nieuwenhuizen cm/01-in; Ghosh et al AJP(06)feb [dynamical framework]; Bertin et al PRL(06) [intensive parameters]; Astumian AJP(06)aug [use of equilibrium theory]; Qiao a0709/PhyA [based on subdynamics]; de Almeida a0806 [quantum]; Bertini et al JSP(09) [macroscopic description of driven diffusive systems]; Hernandez-Lemus & Estrada-Gil EJTP-a0908 [and theory of stochastic processes].

Steady States
@ General references: Penrose & Coveney PRS(94), Evans & Coveney PRS(95) ["canonical" non-equilibrium ensemble]; Rey-Bellet & Thomas CMP(02) [convergence to equilibrium]; Barré et al PRL(02) [as equilibrium of effective dynamics]; Dewar JPA(03) [properties, and information theory]; Eckmann mp/03-in; Sasa & Tasaki JSP(06); Zia & Schmittmann JPA(06) [classification]; Maes & van Wieren PRL(06) [time-symmetric fluctuations]; Taniguchi & Cohen JSP(07) [Onsager-Machlup theory, fluctuation theorems]; Abou Salem mp/07 [fluctuations of macroscopic observables]; Blythe PRL(08) [reversibility and heat dissipation]; Taniguchi & Cohen JSP(08) [thermodynamics and fluctuations].
@ Examples: Piasecki & Soto PhyA(06) [and approach]; Mazilu & Williams AJP(09)may [two-temperature linear spin model]; Maes & Netocny a0911 [McLennan ensembles].

Related Topics > s.a. arrow of time; Detailed Balance; ergodic theory; generalized thermodynamics [relativistic]; information.
* Phase transitions: Non-equilibrium phase transitions are situations in which system properties related to non-equilibrium phenomena, such as transport phenomena, undergo sudden changes with the system's parameters; > s.a. critical phenomena.
@ Chaos: Dorfman 99; Klages 07 [and fractal techniques]; > s.a. quantum chaos.
@ Entropy: Holian PRA(86); Kandrup JMP(87); Martyushev et al JPA(07), Maes & Netocny JMP(07) [minimum entropy production].
@ Other topics: Frieden et al PLA(02) [and Fisher information]; van Zon & Cohen PhyA(04) [fluctuations]; Merkli CMP(01)mp/04 [positive commutators, return to equilibrium]; Carati PhyA(05) [entropies from time averages]; Bustamante et al PT(05)jul [small systems]; Lucarini a0710 [response to perturbations, causality]; González & Téllez JPA(09) [organized-disorganized state crossover]; Criado-Sancho et al PLA(09) [flux fluctuation theorem and non-equilibrium thermodynamic potential]; Cramer & Eisert a0911 [relaxation to Gaussin states].
> Examples of phenomena: see dissipation; fokker-planck equation; Relaxation; Self-Organization; superconductivity; temperature; Transport.

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