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

Source: [Bivectorial Nonequilibrium Thermodynamics: Cycle Affinity, Vorticity Potential, and Onsager's Principle](<https://www.sota2.com/research/paper/68fa3e3f1e209131ce8e69fd>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T01:56:10.350Z

Authors: Ying-Jen Yang, Hong Qian

Published: 2020-04-18T17:59:31.000Z

## Abstract

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 $\\nabla\\wedge\\big(\\mathbf{D}^{-1}\\mathbf{b}\\big)$ and vorticity potential $\\mathbf{A}(\\mathbf{x})$ of 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2004.08677>)

[PDF](<https://arxiv.org/pdf/2004.08677.pdf>)