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).