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arXiv · 2603.22284

Precision-Induced Irreversibility in non-Hermitian systems

Luis E. F. Foa Torres·G. Pappas·V. Achilleos·D. Bautista Avilés
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Abstract

Non-Hermitian evolution is mathematically invertible, yet finite dynamic range imposes a sharp operational limit on reversibility. We identify Precision-Induced Irreversibility (PIR): amplification, mode mixing (as warranted by non-normality), and a finite resolution floor -- whether set by numerical precision, detector noise, or environmental fluctuations -- conspire to produce a quantitative predictability horizon $T_{\mathrm{of}}$, 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.

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Luis E. F. Foa Torres, G. Pappas, V. Achilleos, D. Bautista Avilés. 2026-03-23. Precision-Induced Irreversibility in non-Hermitian systems. https://doi.org/10.1103/mrmj-59p6

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