Statistical formulation of Onsager-Machlup variational principle

TL;DR

This paper reformulates the Onsager-Machlup variational principle to include thermal fluctuations, enabling derivation of dynamical properties like diffusion constants in soft and active matter systems.

Contribution

It introduces a statistical formulation of OMVP that incorporates thermal fluctuations and demonstrates its application to Brownian motion in viscous fluids and shear flows.

Findings

Successfully derived diffusion constant of Brownian particle via maximization of the modified OMVP.

Applied the formulation to non-equilibrium steady shear flow systems.

Discussed potential extensions to active matter systems.

Abstract

Onsager's variational principle (OVP) provides us with a systematic way to derive dynamical equations for various soft matter and active matter. By reformulating the Onsager-Machlup variational principle (OMVP), which is a time-global principle, we propose a new method to incorporate thermal fluctuations. To demonstrate the utility of the statistical formulation of OMVP (SOMVP), we obtain the diffusion constant of a Brownian particle embedded in a viscous fluid only by maximizing the modified Onsager-Machlup integral for the surrounding fluid. We also apply our formulation to a Brownian particle in a steady shear flow, which is a typical example of a non-equilibrium system. Possible extensions of our formulation to internally driven active systems are discussed.