Bivectorial Mesoscopic Nonequilibrium Thermodynamics: Landauer-Bennett-Hill Principle, Cycle Affinity and Vorticity Potential

Ying-Jen Yang, Hong Qian

Published 2020-04-18Version 1

In mesoscopic nonequilibrium thermodynamics (NET), Landauer-Bennett-Hill principle emphasizes the importance of kinetic cycles. For continuous stochastic systems, a NET in phase space is formulated in terms of cycle affinity $\nabla\wedge\big(\mathbf{D}^{-1}\mathbf{b}\big)$ and vorticity $\mathbf{A}(\mathbf{x})$ representing the stationary flux $\mathbf{J}^{*}=\nabla\times\mathbf{A}$. Each bivectorial cycle couples two transport processes represented by vectors and gives rise to Onsager's reciprocality; the scalar product of the two bivectors $\mathbf{A}\cdot\nabla\wedge\big(\mathbf{D}^{-1}\mathbf{b}\big)$ is the rate of local entropy production in the nonequilibrium steady state. An Onsager operator that maps vorticity to cycle affinity is introduced.