Feedback Brownian Ratchets and information

Résumé

Ratchets or Brownian motors can be viewed as controllers that act on stochastic systems with the aim of inducing directed motion through the rectification of fluctuations. In the present thesis, we investigate closed-loop or feedback controlled ratchets, which are those ratchets whose rectification action has an explicit dependence on the state of the system. We have analyzed the dynamics and performance of feedback controlled ratchets focusing on what characterizes them, namely, the use of information about the state of the system. We have shown that this use of information is what allows closed-loop ratchets to increase the performance over their open-loop counterparts. In addition, our research on the effects of time delay in the feedback has revealed a rich dynamics exhibiting multistability and current reversals. These studies of the effects of time delay together with the effects of noise in the feedback have shown the viability of experimental realizations of feedback controlled ratchets. We have also found that the combination of a zero-mean oscillating force with the feedback mechanism leads to the maximum flux that has been achieved in a ratchet device without an a priori bias. On the other hand, in this thesis we have completed the thermody- namics of general feedback controlled systems by computing the entropy reduction when the system is repeatedly operated by the controller. This was the lacking ingredient to establish the thermodynamics of feedback controlled systems, and in particular of Maxwell’s demons. Finally, we present some still open questions and future perspectives in the new emerging field of feedback ratchets.