Covariant Onsager and Onsager-Machlup principles for active and inertial dynamics
Abstract
The Onsager principle provides a variational route to the phenomenological equations of dissipative dynamics through the minimization of the Rayleighian. We develop a covariant formulation of the Onsager principle for active systems, ensuring geometric consistency under coordinate transformations. To further incorporate thermal fluctuations, we formulate the Onsager-Machlup principle for active systems by considering the Onsager-Machlup functional and the corresponding path probability for stochastic trajectories. Requiring that the path probability obeys the detailed fluctuation theorem, we show that the extended Onsager-Machlup theory is consistent with stochastic thermodynamics. Moreover, we incorporate inertia into the variational framework and show that the proper covariant equations follow when the covariant acceleration is held fixed during the variation.
Keywords
Cite
@article{arxiv.2604.22371,
title = {Covariant Onsager and Onsager-Machlup principles for active and inertial dynamics},
author = {Kento Yasuda and Bin Zheng and Zhongqiang Xiong and Zhanglin Hou and Kenta Ishimoto and Xinpeng Xu and David Andelman and Shigeyuki Komura},
journal= {arXiv preprint arXiv:2604.22371},
year = {2026}
}