  We establish a connection between non-Markovianity and negative entropy
production rate for various classes of quantum operations. We analyse several
aspects of unital and thermal operations in connection with resource theories
of purity and thermodynamics. We fully characterize Lindblad operators
corresponding to unital operations. We also characterize the Lindblad dynamics
for a large class of thermal operations. We next generalize the definition of
the entropy production rate for the non-equilibrium case to connect it with the
rate of change of free energy of the system, and establish complementary
relations between non-Markovianity and maximum loss of free energy. We
naturally conclude that non-Markovianity in terms of divisibility breaking is a
necessary resource for the backflow of other resources like purity or free
energy under the corresponding allowed operations.
