General theory of Onsager symmetries for perturbations of equilibrium and nonequilibrium steady states

Journal Article · Mon Nov 01 04:00:00 EST 1993 · Physics of Fluids B; (United States)

DOI:https://doi.org/10.1063/1.860614· OSTI ID:6072387

Krommes, J A; Hu, G ^[1]

---

1. Plasma Physics Laboratory, Princeton University, P.O. Box 451, Princeton, New Jersey 08543 (United States)

The theory of Onsager symmetry is reconsidered from the point of view of its application to nonequilibrium, possibly turbulent steady states. A dynamical formalism based on correlation and response functions is used; understanding of its relationship to more conventional approaches based on entropy production enables one to resolve various confusions about the proper use of the theory, even near thermal equilibrium. Previous claims that kinematic'' flows must be excluded from considerations of Onsager symmetry are refuted by showing that suitably defined reversible and irreversible parts of the Onsager matrix separately obey the appropriate symmetry; fluctuating hydrodynamics serves as an example. It is shown that Onsager symmetries are preserved under arbitrary covariant changes of variables; the Weinhold metric is used as a fundamental tensor. Covariance is used to render moot the controversy over the proper choice of fluxes and forces in neoclassical plasma transport theory. The fundamental distinction between the fully contravariant Onsager matrix [ital L][sup [ital ij]] and its mixed representation [ital L][sup [ital i]][sub [ital j]] is emphasized and used to explain why some previous workers have failed to find Onsager symmetry around turbulent steady states. The generalized Onsager theorem of Dufty and Rubi [Phys. Rev. A [bold 36], 222 (1987)] is reviewed. An explicitly soluble Langevin problem is shown to violate Onsager's original symmetry but to obey the generalized theorem. The physical content of the generalized Onsager symmetry is discussed from the point of view of Nose--Hoover dynamics. A set of extended Graham--Haken potential conditions are derived for Fokker--Planck models and shown to be consistent with the generalized Onsager relations.

• OSTI ID: 6072387
• Journal Information: Physics of Fluids B; (United States), Journal Name: Physics of Fluids B; (United States) Vol. 5:11; ISSN 0899-8221; ISSN PFBPEI
• Country of Publication: United States
• Language: English

Related Subjects

661300 -- Other Aspects of Physical Science-- (1992-)
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700330* -- Plasma Kinetics
Transport
& Impurities-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CORRELATION FUNCTIONS
EQUILIBRIUM
FUNCTIONS
IRREVERSIBLE PROCESSES
MARKOV PROCESS
MATRICES
ONSAGER RELATIONS
RESPONSE FUNCTIONS
STEADY-STATE CONDITIONS
STOCHASTIC PROCESSES
THERMODYNAMICS
TRANSPORT THEORY
TURBULENCE