  Active systems are comprised of constituents with interactions that are
generically non-reciprocal in nature. Such non-reciprocity often gives rise to
situations where conflicting objectives exist, such as in the case of a
predator pursuing its prey, while the prey attempts to evade capture. This
situation is somewhat reminiscent of those encountered in geometrically
frustrated systems where conflicting objectives also exist, which result in the
absence of configurations that simultaneously minimize all interaction
energies. In the latter, a rich variety of exotic phenomena are known to arise
due to the presence of accidental degeneracy of ground states. In this paper,
we establish a direct analogy between these two classes of systems. The analogy
is based on the observation that non-reciprocally interacting systems with
anti-symmetric coupling and geometrically frustrated systems have in common
that they both exhibit marginal orbits, which can be regarded as a dynamical
system counterpart of accidentally degenerate ground states. The former is
shown by proving a Liouville-type theorem. These ''accidental degeneracies'' of
orbits are shown to often get ''lifted'' by stochastic noise or weak random
disorder due to the emergent ''entropic force'' to give rise to a noise-induced
spontaneous symmetry breaking, in a similar manner to the order-by-disorder
phenomena known to occur in geometrically frustrated systems. Furthermore, we
report numerical evidence of a non-reciprocity-induced spin-glass-like state
that exhibits a short-ranged spatial correlation (with stretched exponential
decay) and an algebraic temporal correlation associated with the aging effect.
Our work establishes an unexpected connection between the physics of complex
magnetic materials and non-reciprocal matter, offering a fresh and valuable
perspective for comprehending the latter.
