  The sum of the average work dissipated plus the information gained during a
thermodynamic process with discrete feedback must exceed zero. We demonstrate
that the minimum value of zero is attained only by feedback-reversible
processes that are indistinguishable from their time-reversal, thereby
extending the notion of thermodynamic reversibility to feedback processes. In
addition, we prove that in every realization of a feedback-reversible process
the sum of the work dissipated and change in uncertainty is zero.
