Phase transitions and thermodynamic cycles in the broken PT-regime

We propose a new type of quantum thermodynamic cycle whose efficiency is greater than the one of the classical Carnot cycle for the same conditions for a system when viewed as homogeneous. In our model this type of cycle only exists in the low temperature regime in the spontaneously broken parity-time-reversal (PT) symmetry regime of a non-Hermitian quantum theory and does not manifest in the PT-symmetric regime. We discuss this effect for an ensemble based on a model of a single boson coupled in a non-Hermitian way to a bath of different types of bosons with and without a time-dependent boundary. The cycle can not be set up when considering our system as heterogeneous, i.e. undergoing a first order phase transition. Within that interpretation we find that the entropy is vanishing throughout the spontaneously broken PT-regime.