In the present paper, the problem of selecting priors for continuous-time processes is approached using the MaxEnt paradigm. First, assuming stationarity and Gaussianity, a suitable definition of differential entropy rate is introduced. Second, it is observed that a prior on the smoothness of the signal can be rather naturally expressed through the variances of the process and some of its derivatives. Finally, under some technical assumption, the expression of the MaxEnt spectrum is derived.