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].

Relativistic Thermodynamics and Statistical Mechanics > s.a. 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 quantities 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); 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; Ares de Parga & López-Carrera PhyA(09) [Nakamura formalism]; Dunkel et al a0902 [using past light cone].
@ 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]; Klein & Collas CQG(09)-a0810 [with timelike Killing fields].
@ Quantum gravity-motivated: Fityo PLA(08)-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.
@ 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. gases; thermodynamic 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].
> Other generalizations: see non-equilibrium statistical mechanics and thermodynamics; non-extensive statistics.

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