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The information on a quantum process acquired through measurements plays acrucial role in the determination of its non-equilibrium thermodynamicproperties. We report on the experimental inference of the stochastic entropyproduction rate for a continuously monitored mesoscopic quantum system. Weconsider an optomechanical system subjected to continuous displacement Gaussianmeasurements and characterise the entropy production rate of the individualtrajectories followed by the system in its stochastic dynamics, employing aphase-space description in terms of the Wigner entropy. Owing to the specificregime of our experiment, we are able to single out the informationalcontribution to the entropy production arising from conditioning the state onthe measurement outcomes. Our experiment embodies a significant step towardsthe demonstration of full-scale control of fundamental thermodynamic processesat the mesoscopic quantum scale.

Experimental assessment of entropy production in a continuously measured mechanical resonator