Symmetry-Enforced Non-Hermitian Jarzynski Equality in an SU(2)-Rotated Family of Hybrid \mathcal{P}\mathcal{T}-\mathcal{A}\mathcal{P}\mathcal{T} Systems

Abstract

The Jarzynski equality is a cornerstone of nonequilibrium thermodynamics, linking work statistics to equilibrium freeenergy differences. Although it has been extensively verified in classical and quantum Hermitian settings, its status in non-Hermitian dynamics remains under debate. Here we show that, in a post-selected no-quantum-jump framework, a conditional non-Hermitian Jarzynski equality holds when the transition probabilities obey a parity-exchange symmetry. We study a constructed family of two-level hybrid Hamiltonians formed as linear combinations of parity-time (\mathcal{P}\mathcal{T}) and anti-parity-time (\mathcal{A}\mathcal{P}\mathcal{T}) symmetric terms, and demonstrate using complementary geometric and algebraic arguments that the parity-exchange symmetry persists throughout the corresponding SU(2)-rotated orbit. Relative to previous \mathcal{P}\mathcal{T}-focused conditional Jarzynski equality results, the advance here is an extension of the symmetry criterion from the isolated \mathcal{P}\mathcal{T} endpoint to a broader \mathcal{P}\mathcal{T}-\mathcal{A}\mathcal{P}\mathcal{T} hybrid family. Experimentally, we implement three representative points, θ_k = 0, π/4, π/2, in a single trapped ¹⁷¹Yb⁺ ion and measure the resulting work distributions under cyclic protocols with ΔF = 0, confirming the predicted symmetry criterion at those points. Our results establish a symmetry-based extension of the conditional non-Hermitian Jarzynski relation within this restricted two-level setting.

Keywords

Jarzynski equality / non-Hermitian dynamics / \mathcal{P}\mathcal{T} and \mathcal{A}\mathcal{P}\mathcal{T} symmetry / parity-exchange symmetry / trapped ion

RIGHTS & PERMISSIONS

Higher Education Press 2026

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