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arXiv · 2604.22371

Covariant Onsager and Onsager-Machlup principles for active and inertial dynamics

Kento Yasuda·Bin Zheng·Zhongqiang Xiong·Zhanglin Hou·Kenta Ishimoto·Xinpeng Xu·David Andelman·Shigeyuki Komura
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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 and inertial systems, ensuring geometric consistency under coordinate transformations. To further incorporate thermal fluctuations, we formulate the Onsager-Machlup principle for active and inertial 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. The extended OP and OMP offer a unified and useful variational framework for deriving the dynamical equations of active and inertial systems.

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Kento Yasuda, Bin Zheng, Zhongqiang Xiong, Zhanglin Hou, Kenta Ishimoto, Xinpeng Xu, David Andelman, Shigeyuki Komura. 2026-04-24. Covariant Onsager and Onsager-Machlup principles for active and inertial dynamics. https://doi.org/10.1088/1674-1056%2Fae8da8

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