  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.
