  An exact canonical master equation of the Lindblad form is derived for a
central spin interacting uniformly with a sea of completely unpolarized spins.
The Kraus operators for the dynamical map are also derived. The
non-Markovianity of the dynamics in terms of the divisibility breaking of the
dynamical map and increase of the trace distance fidelity between quantum
states is shown. Moreover, it is observed that the irreversible entropy
production rate is always negative (for a fixed initial state) whenever the
dynamics exhibits non-Markovian behavior. In continuation with the study of
witnessing non-Markovianity, it is shown that the positive rate of change of
the purity of the central qubit is a faithful indicator of the non-Markovian
information back flow. Given the experimental feasibility of measuring the
purity of a quantum state, a possibility of experimental demonstration of
non-Markovianity and the negative irreversible entropy production rate is
addressed. This gives the present work considerable practical importance for
detecting the non-Markovianity and the negative irreversible entropy production
rate.
