  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.
