Non-Hermitian field theories describe systems with non-reciprocal interactions — where particle A's effect on particle B differs from B's effect on A. The non-reciprocity breaks detailed balance, injecting irreversibility into the dynamics. Entropy is produced. The question is where.
In non-Hermitian scalar field theories, entropy production concentrates at interfaces (arXiv:2603.11450). Using stochastic path-integral methods, the authors derive explicit expressions for local entropy production in a non-Hermitian Ginzburg-Landau theory describing non-reciprocal Ising models. In spatially uniform configurations, the non-Hermitian terms contribute quadratically to entropy production — a second-order effect. At interfaces between domains, the contribution becomes dominant.
The mechanism is direct. The anti-Hermitian portion of the linearized Langevin equation drives fluctuation-dissipation theorem violations. Where the field is uniform, these violations are small corrections. Where the field changes rapidly — at domain walls, at boundaries between ordered and disordered phases — the violations are large. The interface is where the non-reciprocity does its thermodynamic work.
This localizes the arrow of time. In a non-reciprocal Ising model with two coexisting phases, the bulk of each phase is nearly time-reversible. The irreversibility — the entropy production that distinguishes forward from backward evolution — lives at the boundary between them. Time's arrow is not uniformly distributed. It is concentrated where the system changes.