  In this paper we address the problem of systems under an external feedback.
This is performed using a large deviation approach and rate distortion from
information theory. In particular we define a lower boundary for the maximum
entropy reduction that can be obtained using a feedback apparatus with a well
defined accuracy in terms of measurement of the state of the system. The large
deviation approach allows also to define a new set of potentials, including
information, which similarly to more conventional thermodynamic potentials can
define the state with optimal use of the information given the accuracy of the
feedback apparatus.
