The Flux Hypothesis for Odd Transport Phenomena

TL;DR

This paper extends Onsager's regression hypothesis to include odd transport phenomena, deriving new relations and verifying them through models and simulations in chiral active matter.

Contribution

It introduces the flux hypothesis, generalizing the regression hypothesis to account for odd transport, and derives related Green-Kubo and reciprocal relations.

Findings

Derived Green-Kubo relation for odd collective diffusion.

Verified the relation through analytical models.

Confirmed results with molecular dynamics simulations.

Abstract

Onsager's regression hypothesis makes a fundamental connection between macroscopic transport phenomena and the average relaxation of spontaneous microscopic fluctuations. This relaxation, however, is agnostic to odd transport phenomena, in which fluxes run orthogonal to the gradients driving them. To account for odd transport, we generalize the regression hypothesis, postulating that macroscopic linear constitutive laws are, on average, obeyed by microscopic fluctuations, whether they contribute to relaxation or not. From this "flux hypothesis," Green-Kubo and reciprocal relations follow, elucidating the separate roles of broken time-reversal and parity symmetries underlying various odd transport coefficients. As an application, we derive and verify the Green-Kubo relation for odd collective diffusion in chiral active matter, first in an analytically-tractable model and subsequently through molecular dynamics simulations of concentrated active spinners.