Changing the state of a memristive system with white noise

Can we change the average state of a resistor by simply applying white noise? We show that the answer to this question is positive if the resistor has memory of its past dynamics (a memristive system). We also prove that, if the memory arises only from the charge flowing through the resistor -- an ideal memristor -- then the current flowing through such memristor can not charge a capacitor connected in series, and therefore cannot produce useful work. Moreover, the memristive system may skew the charge probability density on the capacitor, an effect which can be measured experimentally.