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We investigate stochastic entropy production in a two-level quantum systemthat performs Rabi oscillations while undergoing quantum measurement broughtabout by continuous random disturbance by an external measuring device orenvironment. The dynamics produce quantum Zeno and anti-Zeno effects forcertain measurement regimes, and the stochastic entropy production is a measureof the irreversibility of the behaviour. When the strength of the measurementdisturbance is time-dependent, the stochastic entropy production separates intothree components. Two represent relaxational behaviour, one being specific tosystems represented by coordinates that are odd under time reversal symmetry,and a third characterises the nonequilibrium stationary state arising frombreakage of detailed balance in the dynamics. The study illustrates how theideas of stochastic thermodynamics may be applied in similar ways to bothquantum and classical systems.

Three components of stochastic entropy production associated with the quantum Zeno and anti-Zeno effects