  Diffusive transport is characterized by a diffusivity tensor which may, in
general, contain both a symmetric and an antisymmetric component. Although the
latter is often neglected, we derive Green-Kubo relations showing it to be a
general characteristic of random motion breaking time-reversal and parity
symmetries, as encountered in chiral active matter. In analogy with the
so-called odd viscosity appearing in chiral active fluids, we term this
component the odd diffusivity. We show how odd diffusivity emerges in a chiral
random walk model, and demonstrate the applicability of the Green-Kubo
relations through molecular dynamics simulations of a passive tracer particle
diffusing in a chiral active bath.
