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We revisit the model of a Brownian particle in a heat bath submitted to anactively controlled force proportional to the velocity that leads to thermalnoise reduction (cold damping). We investigate the influence of the continuousfeedback on the fluctuations of the total entropy production and show that theexplicit expression of the detailed fluctuation theorem involves differentdynamics and observables in the forward and backward processes. As anillustration, we study the analytically solvable case of a harmonic oscillatorand calculate the characteristic function of the entropy production in anonequilibrium steady state. We then determine the corresponding largedeviation function which results from an unusual interplay between 'boundary'and 'bulk' contributions.

Entropy production and fluctuation theorems under feedback control: the molecular refrigerator model revisited