Coarse-graining interpretation of diagonal-noise models for odd diffusive particles

Determine whether Langevin equations with a diagonal noise matrix, as used in previous simulations of odd diffusive particles, can arise as the outcome of a coarse-graining procedure.

Background

The paper develops an oblique Mori–Zwanzig projection formalism for deriving dynamically consistent generalized Langevin equations in far-from-equilibrium systems. For the passive tracer in a chiral active bath, the resulting fluctuating-force correlation matrix is antisymmetric, so the authors argue that the tracer cannot be faithfully represented by a simple Markovian Langevin equation with diagonal noise.

The authors note that earlier studies have nevertheless simulated odd diffusive particles using Langevin equations with diagonal noise matrices. The unresolved issue is whether such models can actually be obtained from a valid coarse-graining procedure, rather than serving only as phenomenological descriptions.