For continuously monitored Gaussian quantum systems, the entropy production rate equals the unmonitored rate plus the rate of minus the mutual information between the phase-space position and the measurement outcomes.
Fluctuations and Irreversible Thermodynamics,
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Entropy Production in Continuously Measured Gaussian Quantum Systems
For continuously monitored Gaussian quantum systems, the entropy production rate equals the unmonitored rate plus the rate of minus the mutual information between the phase-space position and the measurement outcomes.