Breaking conservation law enables steady-state entanglement out of equilibrium

We show how entangled steady states can be prepared by purely dissipative dynamics in a system coupled to a thermal environment. While entanglement is hindered by thermalization when the system and environment exchange a conserved quantity, we demonstrate that breaking this conservation law through the system-environment interaction drives the system to a nonequilibrium steady state. Such an interaction will generate multiple competing equilibration channels, effectively mimicking baths at distinct chemical potentials. When the environment also supports long-range correlations, these channels mediate nonlocal dissipation capable of generating entanglement. We illustrate the scheme in a model of two nitrogen-vacancy (NV) centers weakly coupled to a spin-pumped magnet, where tuneable magnon excitations enable steady-state entanglement over finite distances. Our results identifies a general mechanism for dissipative entanglement generation, rooted in the conservation structure and environmental correlations rather than fine-tuned coherent control or active driving.