Jarzynski equality in $\mathcal{PT}$-symmetric quantum mechanics

TL;DR

This paper extends the quantum Jarzynski equality to $ ext{PT}$-symmetric quantum mechanics, showing it holds in the unbroken regime but fails in the broken regime, with implications demonstrated in optical waveguide systems.

Contribution

It demonstrates the generalization of the Jarzynski equality to $ ext{PT}$-symmetric quantum systems and explores the thermodynamic behavior across the phase transition.

Findings

Jarzynski equality holds in unbroken $ ext{PT}$-symmetry regime

Equality fails in broken $ ext{PT}$-symmetry regime due to norm non-preservation

Irreversible work diverges at the phase transition point

Abstract

We show that the quantum Jarzynski equality generalizes to $\mathcal{PT}$-symmetric quantum mechanics with unbroken $\mathcal{PT}$-symmetry. In the regime of broken $\mathcal{PT}$-symmetry the Jarzynski equality does not hold as also the $\mathcal{CPT}$-norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system -- two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken $\mathcal{PT}$-symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.