Impact of non-Markovian evolution on characterizations of quantum thermodynamics

Abstract: Here we study the impact of non-Markovian evolution on prominent characteristics of quantum thermodynamics, such as ergotropy and power. These are benchmarked by the behavior of the quantum speed limit time. We make use of both geometric-based, particularly quantum Fisher and Wigner-Yanase information metric, and physical properties based-measures, particularly relative purity measure and relative entropy of coherence measure, to compute the quantum speed limit time. A simple non-Markovian model of a qubit in a bosonic bath exhibiting non-Markovian amplitude damping evolution is considered, which, from the quantum thermodynamic perspective with finite initial ergotropy, can be envisaged as a quantum battery. To this end, we explore the connections between the physical properties-based measures of quantum speed limit time and the coherent component of ergotropy. The non-Markovian evolution is shown to impact the recharging process of the quantum battery. Further, a connection between the discharging-charging cycle of the quantum battery and the geometric measures of quantum speed limit time is observed.