Non-Equilibrium Statistical Mechanics and Thermodynamics  

In General > s.a. quantum statistical mechanics; statistical mechanics [approach to equilibrium] / states and systems.
* 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 ρ), and estimate the fluctuations.
* 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; More recently computer simulations have been carried out, e.g., using cellular automata (G Jona-Lasinio, C Laudin & M-E Vares).
* Issue: Many results on non-equilibrium systems have been derived using arguments in which microscopic fluctuations are not reliably treated, for lack of a good statistical theory even in the steady-state case; For example, Fourier's law that describes heat transfer in a normal wire fails at the nanoscale.
* Features: Far from equilibrium a system can develop spontaneous ordered structures with specific patterns (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; In lattice systems dynamics can be studied using numerical techniques such as matrix-product-state-based methods, for continuum systems Hamiltonian truncation methods can be applied.
@ Books: de Groot & Mazur 62; Balescu 75, 97; Lavenda 85; Keizer 87; Brenig 89; Gaspard 98; Eu 98; Zwanzig 01; Chen 03 [without the assumption of molecular chaos]; Le Bellac et al 04; Ebeling & Sokolov 05; Öttinger 05; Mazenko 07; Evans & Morriss 07 [liquids]; Balakrishnan 08 [II/III]; Lebon et al 08; Ódor 08; Streater 09 [stochastic approach]; Pottier 09 [and linear irreversible processes, r JSP(11)]; Krapivsky et al 10 [r JSP(11)]; Kamenev 11 [field-theoretical methods, r PT(12)nov]; Attard 12; Wio et al 12; Gallavotti 14-a1311 [and chaos, irreversibility]; Livi & Politi 17.
@ Overviews: Ruelle PhyA(99); Gorban & Karlin cm/03 [geometrical]; Ruelle PT(04)may; Pokrovski EJP(05); Abou Salem mp/06 [quantum, and thermodyamics]; Gaspard PhyA(06); Maes et al LNM(09)-mp/07; Zia JSP(10) [and KLS model]; Jaksic et al JMP(14)#7; Ribeiro et al AJP(16)dec-a1601 [small quantum systems, pedagogical introduction].

Frameworks, Tools > s.a. computational physics.
@ General references: Schlögl PRP(80) [stochastic measures]; Gaveau & Schulman PLA(97) [master equation]; Nieuwenhuizen cm/01-MG9; Ghosh et al AJP(06)feb [dynamical framework]; Bertin et al PRL(06) [intensive parameters]; Astumian AJP(06)aug [use of equilibrium theory]; Hernández-Lemus & EJTP(08)-a0908 [and theory of stochastic processes]; Sadhukhan & Bhattacharjee JPA(10); Bertini et al JSP(12) [work and thermodynamic transformations]; Kleeman JSP(15)-a1307 [path-integral formalism]; Etkin a1404 [from thermokinetics to thermostatics]; Brandão et al PRL(13) [resource theory]; Duong a1412; Gay-Balmaz & Yoshimura a1510 [Lagrangian formalism]; Pavelka et al PhyD(16)-a1512 [Poisson brackets]; Gay-Balmaz & Yoshimura JMP(18)-a1704 [Dirac structures], Ent(19)-a1904 [variational formulation, rev], a1904 [variational to bracket formulations]; Aibara et al PTEP(19)-a1807 [gravity analog model].
@ Specific techniques: Qiao a0709/PhyA [based on subdynamics]; Bertini et al JSP(09) [macroscopic description of driven diffusive systems]; Parmeggiani Phy(12) [new methods]; Deffner & Lutz PRE(13)-a1212 [far from equilibrium, Bures angle and thermodynamic length]; Rakovszky et al NPB(16)-a1607 [Hamiltonian truncation approach]; te Vrugt & Wittkowski a2001 [Mori-Zwanzig projection operator formalism]; Camsari et al a2008 [Non-Equilibrium Green Function method].
> Related topics: see Effective Field Theory; generalized thermodynamics [irreversible]; MaxEnt; stochastic quantization.

Concepts and Phenomena > s.a. arrow of time; Heat Flow; information; Master Equation; states and systems; Transport Phenomena.
* Laws and constraints: There are constraints on the evolution of non-equilibrium systems, that form a new family of second laws.
* 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; quantum phase transitions [dynamical quasicondensation].
* Entropy production: Prigogine suggested that there are two universal behaviors, (i) the entropy production rate decreases when a system approaches a steady state, and (ii) the entropy production rate reaches its minimal value at the steady state.
@ Chaos: Dorfman 99; Klages 07 [transport 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]; Maes PS(12); Lieb & Yngvason PRS(13)-a1305; Wittkowski et al JPA(13) [microscopic approach to entropy production]; Beretta a1312-conf [steepest entropy ascent paths towards the MaxEnt distribution]; Kadanoff a1403 [kinetic entropy, etc]; Brunelli et al a1602 [entropy production in mesoscopic quantum systems]; Camati et al PRL(16) [control by Maxwell's demon]; Šafránek et al a1905 [dynamical coarse-grained entropy]; Dowling et al a2008 [relativistic fluids, second law and relative entropy].
@ Fluctuations: van Zon & Cohen PhyA(04); Lucarini JSP(08)-a0710 [response to perturbations, causality]; Criado-Sancho et al PLA(09) [flux fluctuation theorem and non-equilibrium thermodynamic potential]; Chetrite & Gawedzki JSP(09) [diffusion, Eulerian and Lagrangian pictures, and fluctuation-dissipation relations]; Boksenbojm et al PhyA(10) [work relations and the second law]; Altaner a1210 [Stochastic Thermodynamics approach]; Pagel et al NJP(13)-a1310 [fluctuation relations for harmonic oscillators]; Funo et al PRE(16)-a1609 [small systems, work fluctuation and total entropy production].
@ Related topics: Frieden et al PLA(02) [and Fisher information]; Merkli CMP(01)mp/04 [positive commutators, return to equilibrium]; Carati PhyA(05) [entropies from time averages]; Chiocchetta et al PRB(16)-a1606 [short-time universal exponents, functional renormalization-group approach]; Brandão et al PNAS-a1305 [second laws; s.a. in Bernamonti et al a1803]; > s.a. Detailed Balance; ergodic theory; fokker-planck equation; Multiscale Physics; temperature.

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