The Role of Odd Diffusivity in Multipoint Statistics of State-Dependent Observables
arXiv:2607.26824
The paper demonstrates that the joint statistics of any number of state‑dependent observables are unaffected by the antisymmetric (odd) part of the diffusion tensor, meaning odd diffusivity does not influence multipoint measurements and conventional Langevin dynamics can be used while retaining odd mobility effects.
Abstract
Odd diffusivity is a transverse transport coefficient that appears when time-reversal and parity symmetries are broken. Its most distinctive signature is a probability flux perpendicular to a density gradient, generated by the antisymmetric part of the diffusion tensor. Here we show that for an arbitrary number of state-dependent observables measured at arbitrary times, their joint statistics are independent of the antisymmetric part of the diffusion tensor. Thus, the Lorentz flux does not contribute to any multipoint state-observable measurements. The result clarifies the separate roles of two effects that are often linked together by fluctuation--dissipation relations, i.e., odd mobility and odd diffusivity. This observation demonstrates that the anomalous correlations in odd-diffusive systems originate solely from odd mobility. It also allows the statistics of state-dependent observables in odd-diffusive systems to be computed using conventional Langevin dynamics without the antisymmetric diffusion part while preserving the antisymmetric mobility tensor. It implies that universal relations associated with state-dependent observables alone, such as nonlinear fluctuation--dissipation relations and generalized Green--Kubo relations, remain valid in odd-diffusive systems without modification. We verify our findings through mean back relaxation, the diffusion coefficient, the nonlinear fluctuation--dissipation relation, and a generalized Green--Kubo relation in diverse systems.
15 pages, 4 figures