The working substance fueling a quantum heat engine may contain coherence in its energy basis, depending on the dynamics of the engine cycle. In some models of quantum Otto heat engines, energy coherence has been associated with entropy production and quantum friction. We considered a quantum Otto heat engine operating at finite time. Coherence is generated and the working substance does not reach thermal equilibrium after interacting with the hot heat reservoir, leaving the working substance in a state with residual energy coherence. We observe an interferencelike effect between the residual coherence (after the incomplete thermalization) and the coherence generated in the subsequent finite-time stroke. We introduce analytical expressions highlighting the role of coherence and examine how this dynamical interference effect influences the engine performance. Additionally, in this scenario in which coherence is present along the cycle, we argue that the careful tuning of the cycle parameters may exploit this interference effect and make coherence acts like a dynamical quantum lubricant. To illustrate this, we numerically consider an experimentally feasible example and compare the engine performance to the performance of a similar engine where the residual coherence is completely erased, ruling out the dynamical interference effect.

The extension of quantum thermodynamics to situations that go beyond standard thermodynamic settings comprises an important and interesting aspect of its development. One such situation is the analysis of the thermodynamic consequences of structured environments that induce a non-Markovian dynamics. We study a quantum Otto refrigerator where the standard Markovian cold reservoir is replaced by a specific engineered cold reservoir which may induce a Markovian or non-Markovian dynamics on the quantum refrigerant system. The two dynamical regimes can be interchanged by varying the coupling between the refrigerant and the reservoir. An increase of non-Markovian effects will be related to an increase of the coupling strength, which in turn will make the energy stored in the interaction Hamiltonian, the interaction energy, increasingly relevant. We show how the figures of merit, the coefficient of performance, and the cooling power change for non-negligible interaction energies, discussing how neglecting this effect would lead to an overestimation of the refrigerator performance. Finally, we also consider a numerical simulation of a spin quantum refrigerator with experimentally feasible parameters to better illustrate the non-Markovian effects induced by the engineered cold reservoir. We argue that a moderate non-Markovian dynamics performs better than either a Markovian or a strong non-Markovian regime of operation.