Thermal ratchets with symmetric potentials

It is shown that the directed transport of Brownian particles can be induced by thermal ratchets with symmetric, two-state fluctuating potentials, contorary to an earlier belief that at least three slates are needed for the potential to fluctuate if the potential is symmetric. It is proved that the potential must lack the symmetry of glide reflection in order for the directed movement of particles to occur in a two-state ratchet. Based on this finding, several models with symmetric potentials are constructed to demonstrate the occurrence of the particle flow.