Abstract
We study adaptive control of classical ergodic Hamiltonian systems, where the controlling parameter varies slowly in time and is influenced by the system's state (feedback). An effective adiabatic description is obtained for slow variables of the system. A general limit on the feedback-induced negative-entropy production is uncovered. It relates the quickest negentropy production to fluctuations of the control Hamiltonian. The method deals efficiently with the entropy-information trade-off.