The thermal noise on the nanoscale is so great that moving in a particular direction is as difficult as “walking in a hurricane” or “swimming in molasses”. The theoretical operation of the Brownian motor can be explained by ratchet theory, wherein strong random thermal fluctuations are allowed to move the particle in the desired direction, while energy is expended to counteract forces that would produce motion in the opposite direction. This motion can be both linear and rotational. In the biological sense and in the extent to which this phenomenon appears in nature, this exists as chemical energy is sourced from the molecule adenosine triphosphate (ATP).
The Brownian ratchet is an apparent perpetual motion machine that appears to violate the Second Law of Thermodynamics, but was later debunked upon more detailed analysis by Richard Feynman and other physicists. The difference between real Brownian motors and fictional Brownian ratchets is that only in Brownian motors is there an input of energy in order to provide the necessary force to hold the motor in place to counteract the thermal noise that try to move the motor in the opposite direction.
Because Brownian motors rely on the random nature of thermal noise to achieve directed motion, they are stochastic in nature, in that they can be analysed statistically but not predicted precisely.