Precision-Induced Irreversibility in non-Hermitian systems

TL;DR

This paper introduces the concept of Precision-Induced Irreversibility (PIR) in non-Hermitian systems, showing how finite resolution limits cause a predictability horizon despite mathematical invertibility.

Contribution

It identifies PIR as a fundamental limit to reversibility caused by finite precision, independent of environmental effects or nonlinearities, and characterizes its impact on non-Hermitian dynamics.

Findings

PIR creates a predictability horizon $T_{of}$ where states become indistinguishable.

Reversibility can be restored by removing precision limitations, confirming PIR's role.

Echo-fidelity tests demonstrate the divergence of formal invertibility from physical reversibility.

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.