  Active matter with nonreciprocal interactions is known for its distinctive
dynamics. To shed light on the stationary properties of such systems, we
consider paradigmatic systems of nonreciprocally coupled active
Ornstein-Uhlenbeck particles. For each system, we uniquely decompose the
interparticle force into an energy gradient and a transverse nonconservative
force. We show that the steady-state distribution of positions, which would
only reflect the energy if the noise were thermal, features the transverse
force as an effective potential that stabilizes the energy minima, due to the
persistent noise that propels the particles. We exactly solve the distribution
for nonreciprocal harmonic oscillators and numerically verify it for systems
with more complex couplings. When the breaking of reciprocity in the
interactions produces a transverse force without changing the energy gradient,
we indeed find that the nonreciprocity plays a stabilizing role in the
stationary state.
