Geometric formulation of state-dependent Langevin dynamics using scalar free energy (opens in new tab)

Stochastic dynamics with state-dependent diffusion are widely used for Brownian motion in confined, anisotropic, and hydrodynamically coupled systems. The conventional Langevin formulation includes a spurious drift associated with multiplicative noise, but its free energy generally does not transform as a scalar, meaning that the covariance is not explicit. Here, we formulate a geometrically consistent Langevin equation by introducing a scalar...