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

Exact master equation for a spin interacting with a spin bath: Non-Markovianity and negative entropy production rate