History-dependent Maximum Static Friction and Rectification of a System with a Few Particles in a Periodic Field

History-dependent maximum static friction is investigated using simple models with two and three particles in one-dimensional periodic potentials. In some situations, these systems possess two values of the maximum static friction, with that actually realized being determined by the direction of the slippage relative to the direction of the previous slippage. In particular, the maximum static friction for slippage in a given direction is smaller when the previous slippage was in the same direction than when it was in the opposite direction. Owing to this property, a particle can continue to move in a direction even in the case that it is subject to an external force whose direction change in time as in a ratchet system which is regarded as one of the simplest model of molecular motors.