Generalized Thermodynamics

Extended thermodynamics > s.a. particle statistics [fractional].
* In general: Developed as a way out of the paradox of infinite speed of propagation of heat pulses (parabolic heat conduction equation), i.e., to make it consistent with special relativity; The first parabolic equation was obtained in 1948 by Cattaneo, who introduced a relaxation term in the Fourier law, but this led to other problems; There are now two approaches, rational and irreversible.
@ References: Muller & Ruggeri 93; Pennisi et al mp/07; Carrisi et al a0712 [dense gases and macromolecular fluids].

Non-Equilibrium Statistical Mechanics > s.a. arrow of time; Detailed Balance; information; quantum field theory.
* 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 cy, 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; Streater 95; 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.
@ Framework, tools: Schlögl PRP(80) [stochastic measures]; Gaveau & Schulman PLA(97) [master equation]; Nieuwenhuizen cm/01-in; Ghosh et al AJP(06) [dynamical framework]; Bertin et al PRL(06) [intensive parameters]; Astumian AJP(06) [use of equilibrium theory]; Sasa & Tasaki JSP(06) [steady state]; Qiao a0709 [based on subdynamics]; de Almeida a0806 [quantum].
@ Steady states: Rey-Bellet & Thomas CMP(02) [convergence to equilibrium]; Eckmann mp/03-in; Zia & Schmittmann JPA(06) [classification]; Maes & van Wieren PRL(06) [time-symmetric fluctuations]; Blythe PRL(08) [reversibility and heat dissipation]; Taniguchi & Cohen JSP(08) [thermodynamics and fluctuations].
@ Chaos: Dorfman 99; Klages 07 [and fractal techniques]; > s.a. quantum chaos.
@ Related 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].
> Examples of phenomena: see dissipation; fokker-planck equation; Relaxation; Self-Organization; Transport.

Relativistic Thermodynamics and Statistical Mechanics > s.a. temperature.
* Status: No consensus has been reached on the correct relativistic transformations for thermodynamic quantities.
@ General references: Hamity PR(69); Maartens ap/96-in; ter Haar & Wergeland PRP(71); Cimmelli & Francaviglia GRG(01) [non-viscous, heat-conducting]; Lavagno PLA(02) [non-extensive]; Kuckert AP(02) [covariant equilibrium], mp/02-in [moving frame]; Garcia-Colin & Sandoval-Villalbazo JNT(06)gq/05 [non-equilibrium]; Schieve FP(05) [covariant]; Ares de Parga et al JPA(05); Lehmann JMP(06)mp [equilibrium]; Kowalski et al PRD(07)-a0712; López-Carrera & Ares de Parga PhyA(07) [transformation of canonical distribution function]; Requardt a0801.
@ Covariant entropy: Kaniadakis PRE(02), PRE(05)cm, PhyA(06)ht; Nakamura PLA(06) [finite-volume object].
@ In cosmology/curved spacetime: Tolman 34; Coley PLA(89) [with heat conduction]; Hayward gq/98 [in general relativity]; Vacaru gq/00, AP(01)gq/00; Chrobok & von Borzeszkowski GRG(06) [and spacetime geometry].
@ Quantum gravity-motivated: Fityo a0712 [deformed spaces with minimal length].

Other References
@ General: Tisza 66; Muller & Ruggeri 93 [rational approach]; Treumann PS(99), PS(99) [Lorentzian].
@ Irreversible: Jou et al 93; Chen JMP(00); Vasconcellos et al RNC(01) [non-equilibrium statistical ensemble]; Luzzi et al RNC(06).
@ Microcanonical: Gross & Kenney JChP(05)cm.
@ Non-extensive: Abe & Rajagopal PRL(03) [quantum, second law]; > s.a. entropy, models in statistical mechanics, specific heat, temperature, turbulence.
@ Quantum: Syros LMP(99); Alicki et al OSID(04)qp [and information, Hamiltonian]; Fröhlich et al in(03)mp/04 [with t-dependent forces]; Sukhanov TMP(08) [with quantum effects]; > s.a. systems.
@ Other generalizations: Lavenda NCB(99); Vives & Planes PRL(02) [Tsallis thermodynamics]; Belgiorno JMP(03) [quasi-homogeneous thermodynamics and black holes]; Chavanis PhyA(04) [generalized entropies]

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