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: Müller & Ruggeri 93; Pennisi et al mp/07; Carrisi et al a0712 [dense gases and macromolecular fluids].

Relativistic Thermodynamics and Statistical Mechanics > s.a. heat [conduction]; temperature.
* Status: 2009, The unification of relativity and thermodynamics has long been a subject of considerable debate; The reasons are that (i) Thermodynamic variables are non-local and thus single out a preferred class of hyperplanes in spacetime, and no consensus has been reached on the correct relativistic transformation laws for thermodynamic quantities; (ii) There exist different, seemingly equally plausible ways of defining heat and work in relativistic systems.
* Some approaches: van Kampen covariant theory, Rohrlich proposal, Ares de Parga & López-Carrera [PhyA(07)] proposal.
@ General references: Hamity PR(69); ter Haar & Wergeland PRP(71); Maartens ap/96-ln; Lavagno PLA(02) [non-extensive]; Kuckert mp/02-conf [moving frame]; Garcia-Colin & Sandoval-Villalbazo JNT(06)gq/05 [non-equilibrium]; Ares de Parga et al JPA(05); Lehmann JMP(06)mp [equilibrium]; López-Carrera & Ares de Parga PhyA(07) [transformation of canonical distribution function]; Requardt a0801; Ares de Parga & López-Carrera PhyA(09) [Nakamura formalism]; Dunkel et al NatP(09)-a0902 [using the past light cone]; Bíró & Ván EPL(10) [from special-relativistic hydrodynamics]; Güémez EJP(10) [first law]; Hakim 11 [graduate text]; Przanowski & Tosiek PS(11); Becattini PRL(12)-a1201 [and the stress-energy tensor].
@ Notions of equilibrium: Chirco et al PRD(13)-a1309 [for coupled, parametrized systems]; Becattini et al EPJC(15)-a1403; Chirco et al CQG(16)-a1503 [and time and energy, reparametrization-invariant systems].
@ Covariant entropy: Kaniadakis PRE(02), PRE(05)cm, PhyA(06)ht; Nakamura PLA(06) [finite-volume object].
@ Covariant approach, other: Kuckert AP(02) [covariant equilibrium]; Schieve FP(05); Hosseinzadeh et al PRD(15)-a1506 [and non-commutative space].
@ Types of systems: Cimmelli & Francaviglia GRG(01) [non-viscous, heat-conducting fluids]; Kowalski et al PRD(07)-a0712 [ideal gas]; Tsintsadze & Tsintsadze a1212 [Fermi gas in a strong magnetic field]; Chirco & Josset a1606 [covariant systems with multi-fingered time].
@ 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]; Klein & Collas CQG(09)-a0810 [with timelike Killing fields]; Frřnsdal a1106; Rojas & Arenas a1110 [how thermodynamics is modified when gravity is included]; Rovelli PRD(13)-a1209 [general relativistic]; Becattini APPB(16)-a1606 [equilibrium]; Bianchi et al GRG(17)-a1306 [pure and mixed states].
@ Quantum gravity-motivated: Fityo PLA(08)-a0712 [deformed spaces with minimal length].

Quantum Thermodynamics > s.a. complexity; generalized uncertainty principle.
* Idea: 2015, An emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit, in non-equilibrium situations, and with the full inclusion of quantum effects; Recent efforts in the field have been inspired by quantum information theory and its application to thermodynamic machines with quantum components.
@ Intros and reviews: Vinjanampathy & Anders CP(16)-a1508 [rev]; Millen & Xuereb NJP(16)-a1509 [rev]; Ribeiro et al AJP(16)dec [pedagogical]; Facchi & Garnero a1705-ln [and canonical typicality]; blog Quanta(17)may.
@ General references: Syros LMP(99); Alicki et al OSID(04)qp [and information, Hamiltonian]; Fröhlich et al in(03)mp/04 [with time-dependent forces]; Sukhanov TMP(08) [with quantum effects]; Horodecki & Oppenheim NatC(13)-a1111 [quantum and nano thermodynamics]; Dorner PRL(13) + Mazzola et al PRL(13) + news PhysOrg(13)jul; Kosloff Ent(13)-a1305 [emergence of thermodynamical laws from quantum mechanics]; Brandăo et al PNAS(15)-a1305 [second law]; Binder et al PRE(15)-a1406 [operational thermodynamics of open quantum systems]; Kammerlander & Anders SRep(16)-a1502 [coherence and measurement].
@ Work and the first law: Korzekwa et al NJP(16)-a1506 [work extraction from quantum coherence]; Wehner et al a1506 [and reversibility]; Hossein-Nejad et al NJP-a1507 [bipartite systems, work, heat and entropy production]; Alonso et al PRL(16)-a1508 [weakly measured systems]; Alipour et al a1606.
@ Quantum second law: Ćwikliński et al PRL(15) + Huber Phy(15) [and evolution of quantum coherence]; Alhambra et al a1601 [as an equality]; Iyoda et al a1603 [and fluctuation theorem]; Gherardini et al a1706 [entropy production and irreversibility].
@ Evolution of coherence: Lostaglio et al PRX(15).
> Related topics: see arrow of time; gases; Heat Engines; quantum correlations; Squeezed States; thermodynamic systems.

Other References
@ General: Tisza 66; Müller & Ruggeri 98 [rational approach]; Treumann PS(99), PS(99) [Lorentzian]; Bera et al a1612 [with correlations, universal].
@ Irreversible: Chen JMP(00); Vasconcellos et al RNC(01) [non-equilibrium statistical ensemble]; Luzzi et al RNC(06); Jou et al 10; Gorban et al PhyA(13); Schellstede et al GRG(13) [relativistic]; Hanel a1608 [thermodynamic action principle]..
@ Microcanonical: Gross & Kenney JChP(05)cm.
@ Nanoscale, small-scale systems: Lostaglio et al nComm(15)-a1412 [extended laws]; Halpern a1509-proc [resource theories, physical realizations]; van der Meer et al a1706 [smoothed generalized free energies]; Ciliberto PRX(17) [rev, experimental and theoretical results].
@ Photon gas with invariant energy scale: Das & Roychowdhury PRD(10)-a1002; Zhang et al APP(11)-a1102; Das et al Sigma(14)-a1411; Gorji et al a1606 [in dS and AdS momentum spaces].
@ 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]; Eichhorn & Aurell PS(14) [stochastic thermodynamics].
> Other generalizations: see ideal gas [DSR, etc]; non-equilibrium statistical mechanics and thermodynamics; non-extensive statistics; probability in physics [in general probabilistic theories]; types of entropy [Rényi quantum thermodynamics].


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