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Nonreciprocal interactions are commonplace in continuum-level descriptions ofboth biological and synthetic active matter, yet studies addressing theirimplications for time-reversibility have so far been limited to microscopicmodels. Here, we derive a general expression for the average rate ofinformational entropy production in the most generic mixture of conserved phasefields with nonreciprocal couplings and additive conservative noise. For theparticular case of a binary system with Cahn-Hilliard dynamics augmented bynonreciprocal cross-diffusion terms, we observe a non-trivial scaling of theentropy production rate across a parity-time symmetry breaking phasetransition. We derive a closed-form analytic expression in the weak-noiseregime for the entropy production rate due to the emergence of a macroscopicdynamic phase, showing it can be written in terms of the global polar orderparameter, a measure of parity-time symmetry breaking.

Irreversibility across a nonreciprocal ${\cal PT}$-symmetry-breaking phase transition