  We revisit the model of a Brownian particle in a heat bath submitted to an
actively controlled force proportional to the velocity that leads to thermal
noise reduction (cold damping). We investigate the influence of the continuous
feedback on the fluctuations of the total entropy production and show that the
explicit expression of the detailed fluctuation theorem involves different
dynamics and observables in the forward and backward processes. As an
illustration, we study the analytically solvable case of a harmonic oscillator
and calculate the characteristic function of the entropy production in a
nonequilibrium steady state. We then determine the corresponding large
deviation function which results from an unusual interplay between 'boundary'
and 'bulk' contributions.
