  We study a general model of granular Brownian ratchet consisting of an
asymmetric object moving on a line and surrounded by a two-dimensional granular
gas, which in turn is coupled to an external random driving force. We discuss
the two resulting Boltzmann equations describing the gas and the object in the
dilute limit and obtain a closed system for the first few moments of the system
velocity distributions. Predictions for the net ratchet drift, the variance of
its velocity fluctuations and the transition rates in the Markovian limit, are
compared to numerical simulations and a fair agreement is observed.
