Disordered systems can exhibit a dramatic slowdown of their dynamics called aging. Contrary to the established understanding that this phenomenon is destroyed by nonreciprocal interactions, we here show that the outcome crucially depends on the structure of the system. Unlike previous studies, which focused on random nonsymmetric interactions between simple microscopic components, we investigate a scenario where nonreciprocally coupled agents are macroscopic entities with complex internal dynamics, modeled as two identical spin glasses. This framework could be relevant for many biological systems, in which nonreciprocal interactions can arise at a coarse-grained level. Our dynamical mean-field theory calculations reveal a finite temperature transition from a static disordered phase to a non-time-translationally-invariant regime. Below this transition, mediated by a spectral singularity known as exceptional points, we find macroscopic oscillations superimposed on aging behavior. Asymptotically, the system rotates in the plane spanned by the two lowest energy modes of the uncoupled system. We contrast these results to the case of random nonreciprocity, where aging is suppressed at any finite temperature, and propose that the two cases correspond to two broader classes of systems, with “microscopic” versus “macroscopic” nonreciprocity, with aging surviving only in the second case.

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• Dynamical phase transitions
• Nonequilibrium statistical mechanics
• Disordered systems
• Non-Hermitian systems
• Nonequilibrium systems
• Spin glasses
• Cavity methods
• Dynamical mean field theory