Abstract Touchette:

Stochastic ratchets, or Brownian motors as they are often called, can be viewed from an engineering point of view as controllers that act on a stochastic system - usually a bunch of Brownian particles - in order to induce a directed motion through the rectification of fluctuations. In this talk, I will discuss a particular type of ratchet known as a closed-loop or feedback ratchet, which uses information about the state of the system it controls to guide its action on it. By viewing the ratchet as a Maxwell’s demon, I will show that there exists a direct trade-off between the performance of the feedback ratchet as a rectifier of random motion and the amount of information it uses. This trade-off is related to a general result which puts a limit on the performance of closed-loop controllers, which use information to perform control, in terms of the performance of 'open-loop' controllers, which use no information to perform control.

Joint work with Francisco J. Cao and Manuel Feito (Madrid, Spain).