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]
Main page – Abbreviations – Journals – Comments – Other
sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified
21 jun 2008