Oscillatory dynamics driven by nonreciprocal cross-transport

We show that nonreciprocal cross-transport can generate damped spatiotemporal oscillations in the local concentrations of non-reactive multicomponent systems. Using a minimal two-species model, we analyse the oscillatory relaxation that formally emerges when the cross-coupling coefficients have opposite signs and sufficient magnitude, provided that spatial concentration gradients are initially present. A spectral analysis of the transport operator provides the general condition for the emergence of complex eigenvalues and, in the fully antisymmetric limit, analytical expressions relating the oscillation period and damping to the cross-coupling strength and the size of the spatial domain. We further investigate this mechanism under nonequilibrium forcing by considering a system in which thermodiffusion and thermally driven natural convection act concurrently, and the cross-diffusion matrix serves as the effective cross-transport operator. In this case, thermodiffusion and convection spontaneously generate concentration gradients from initially homogeneous conditions, providing a driven environment in which nonreciprocal cross-transport can produce oscillatory concentration dynamics. This framework is discussed in connection with oscillatory scenarios recently observed in thermodiffusive multicomponent systems.