Multicomponent active diffusion

Nonreciprocal interactions are ubiquitous in the natural and living world and can endow systems with properties that have no analog in passive materials. A familiar example of a nonreciprocal interaction is the so-called "predator-prey" interaction whereby one entity (the predator) feels an attractive force towards the other while the other (the prey) is repelled. These effective nonreciprocal interactions can emerge from a host of complex factors and can have far-reaching implications on collective phenomena, phase transitions, and pattern formation. In this talk, we present a dynamical framework for determining the stability of multicomponent active systems. We present phenomenological linear transport relations and derive Green-Kubo relations for the linear transport coefficients that govern the stability of these nonequilibrium systems. For a large class of systems, we can further relate these transport coefficients to mechanical variables, providing a simple criterion for the emergence of traveling phases. Our perspective thus provides a multiscale framework for understanding nonreciprocal phase transitions with multiple conserved order parameters. We demonstrate the utility of this perspective by applying it to two model active systems and predicting the emergence of both stationary and traveling phase transitions.