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

TL;DR

This paper derives an exact non-Markovian master equation for a central spin coupled to a spin bath, showing that non-Markovianity correlates with negative entropy production and proposing experimentally accessible indicators.

Contribution

It provides an exact Lindblad-form master equation for a spin-bath system and links non-Markovianity with negative entropy production, including practical measurement strategies.

Findings

Non-Markovian dynamics cause negative entropy production rate.

Positive purity change indicates non-Markovian information backflow.

Experimental feasibility of detecting non-Markovianity and entropy rate is discussed.

Abstract

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.