Links between Dissipation and R\'{e}nyi Divergences in $\mathcal{PT}$-Symmetric Quantum Mechanics

Thermodynamics and information theory have been intimately related since the times of Maxwell and Boltzmann. Recently it was shown that the dissipated work in an arbitrary non-equilibrium process is related to the R\'{e}nyi divergences between two states along the forward and reversed dynamics. Here we show that the relation between dissipated work and Renyi divergences generalizes to $\mathcal{PT}$-symmetric quantum mechanics with unbroken $\mathcal{PT}$ symmetry. In the regime of broken $\mathcal{PT}$ symmetry, the relation between dissipated work and Renyi divergences does not hold as the norm is not preserved during the dynamics. This finding is illustrated for an experimentally relevant system of two-coupled cavities.