Quantum thermodynamics aspects with a thermal reservoir based on $\mathcal{PT}$-symmetric Hamiltonians

We present results concerning aspects of quantum thermodynamics under the background of non-Hermitian quantum mechanics for the dynamics of a quantum harmonic oscillator. Since a better control over the parameters in quantum thermodynamics processes is desired, we use concepts from collisional model to introduce a simple prototype of thermal reservoir based on $\mathcal{PT}$-symmetric Hamiltonians and study its effects under the thermalization process of a single harmonic oscillator prepared in a displaced thermal state. We verify that controlling the $\mathcal{PT}$-symmetric features of the reservoir allows to reverse the heat flow between system and reservoir, as well as to preserve the coherence over a longer period of time and reduce the entropy production. Furthermore, we considered a modified quantum Otto cycle in which the standard hot thermal reservoir is replaced by the thermal reservoir based on $\mathcal{PT}$-symmetric Hamiltonians. By defining an effective temperature depending on the $\mathcal{PT}$-symmetric parameter, it is possible to interchange the quantum Otto cycle configuration from engine to refrigerator by varying the $\mathcal{PT}$-symmetric parameter. Our results indicate that $\mathcal{PT}$-symmetric effects could be useful to achieve an improvement in quantum thermodynamics protocols such as coherence protection and entropy production reduction.