In his famous lectures Richard Feynman discussed the impossibility to violate the second law of thermodynamics by a ratchet mechanism. The simplest model for a ratchet is an overdamped Brownian particle in an asymmetric but spatially periodic potential (with asymmetry and period L). Due to the fluctuating force caused by the pushing molecules of the surrounding fluid or gas the Brownian particle may overcome the potential barrier moving to the left or to the right. The probabilities for both directions are equal. Thus on average the particle does not move. Hence building a motor which turns thermal energy into mechanical work from a single heath bath is impossible.
But the ratchet can be turned into a so-called a Brownian motor that
seems to violate the second law of thermodynamics. The idea is to turn the
ratchet potential periodically on and off with a frequency
As long as the ratchet potential is off the particle will move diffusively
according to a (biased) random walk, leading to a variance in position of
and a mean position of , where
Where does the energy come from leading to a drift against the external force? The energy does not come from the heath bath but from the ratchet potential when it is switched on. At that moment the potential energy of the particle will be suddenly increased. In the simulation this can be seen by a sudden increase of the energy bar. But most of the energy pushed into the system will be just dissipated into the heath bath due to the relaxation of the particle into a potential minima. Only a tiny portion will be used for doing work. Thus a Brownian motor does not violate any law of thermodynamics it only turns one type of work into another one. Nevertheless the fluctuating force due to the heath bath is essential for a Brownian motor.
For more details and possible applications in biology and chemistry read the
following review article:
R.D. Astumian: Thermodynamics and Kinetics of a Brownian Motor, Science 276, p. 917-922 (1997).