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

TL;DR

This paper extends Onsager and Onsager-Machlup principles to active and inertial systems, ensuring geometric consistency and stochastic thermodynamics compatibility.

Contribution

It develops a covariant formulation of Onsager principles for active systems, including thermal fluctuations and inertia, with a focus on geometric and thermodynamic consistency.

Findings

Covariant Onsager principle formulated for active systems.

Onsager-Machlup functional extended to include active fluctuations.

Inertia incorporated into the variational framework with covariant acceleration.

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.