  Newton's third law, actio = reactio, is a foundational statement of classical
mechanics. However, in natural and living systems, this law appears to be
routinely violated for constituents interacting in a nonequilibrium
environment. Here, we use computer simulations to explore the macroscopic phase
behavior implications of breaking microscopic interaction reciprocity for a
simple model system. We consider a binary mixture of attractive particles and
introduce a parameter which is a continuous measure of the degree to which
interaction reciprocity is broken. In the reciprocal limit, the species are
indistinguishable and the system phase separates into domains with distinct
densities and identical compositions. Increasing nonreciprocity is found to
drive the system to explore a rich assortment of phases, including phases with
strong composition asymmetries and three-phase coexistence. Many of the states
induced by these forces, including traveling crystals and liquids, have no
equilibrium analogue. By mapping the complete phase diagram for this model
system and characterizing these unique phases, our findings offer a concrete
path forward towards understanding how nonreciprocity shapes the structures
found in living systems and how this might be leveraged in the design of
synthetic materials.
