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

Abstract

We show that the quantum Jarzynski equality generalizes to $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics with unbroken $\mathcal{P}\mathcal{T}$-symmetry. In the regime of broken $\mathcal{P}\mathcal{T}$-symmetry the Jarzynski equality does not hold as also the $\mathcal{C}\mathcal{P}\mathcal{T}$-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 $\mathcal{P}\mathcal{T}$-symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.

arXiv comment5 pages, 2 figures; Published version

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