Bivectorial Nonequilibrium Thermodynamics: Cycle Affinity, Vorticity Potential, and Onsager’s Principle

We generalize an idea in the works of Landauer and Bennett on computations, and Hill’s in chemical kinetics, to emphasize the importance of kinetic cycles in mesoscopic nonequilibrium thermodynamics (NET). For continuous stochastic systems, a NET in phase space is formulated in terms of cycle affini...

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Bibliographic Details
Published in:Journal of statistical physics 2021-03, Vol.182 (3), Article 46
Main Authors: Yang, Ying-Jen, Qian, Hong
Format: Article
Language:English
Subjects:
Affinity
Chemical reaction, Rate of
Mathematical and Computational Physics
Nonequilibrium thermodynamics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Reaction kinetics
Statistical Physics and Dynamical Systems
Stochastic systems
Theoretical
Thermodynamics
Vorticity
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Summary:We generalize an idea in the works of Landauer and Bennett on computations, and Hill’s in chemical kinetics, to emphasize the importance of kinetic cycles in mesoscopic nonequilibrium thermodynamics (NET). For continuous stochastic systems, a NET in phase space is formulated in terms of cycle affinity ∇ ∧ ( D - 1 b ) and vorticity potential A ( x ) of the stationary flux J ∗ = ∇ × A . Each bivectorial cycle couples two transport processes represented by vectors and gives rise to Onsager’s notion of reciprocality; the scalar product of the two bivectors A · ∇ ∧ ( D - 1 b ) is the rate of local entropy production in the nonequilibrium steady state. An Onsager operator that relates vorticity to cycle affinity is introduced.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-021-02723-3