Precision-induced irreversibility in non-Hermitian systems
Phys. Rev. A 114, 012207 – Published 13 July, 2026
DOI: https://doi.org/10.1103/mrmj-59p6
Abstract
Non-Hermitian evolution is mathematically invertible, yet finite dynamic range imposes a sharp operational limit on reversibility. We identify precision-induced irreversibility: Amplification, mode mixing (as warranted by non-normality), and a finite resolution floor—whether set by detector noise, environmental fluctuations, or numerical precision—conspire to produce a quantitative predictability horizon , beyond which distinct states collapse onto identical representations. Within the effective non-Hermitian description, the mechanism requires neither environmental decoherence nor nonlinear dynamics; remove any ingredient and reversibility can be restored. Echo-fidelity tests confirm this transition across arbitrary-precision arithmetic and hardware, revealing where formal invertibility and physical reversibility diverge.
