  Biological and engineered systems operate by coupling function to the
transfer of heat and/or particles down a thermal or chemical gradient. In
idealized \textit{deterministically} driven systems, thermodynamic control can
be exerted reversibly, with no entropy production, as long as the rate of the
protocol is made slow compared to the equilibration time of the system. Here we
consider \textit{fully realizable, entropically driven} systems where the
control parameters themselves obey rules that are reversible and that acquire
directionality in time solely through dissipation. We show that when such a
system moves in a directed way through thermodynamic space, it must produce
entropy that is on average larger than its generalized displacement as measured
by the Fisher information metric. This distance measure is sub-extensive but
cannot be made small by slowing the rate of the protocol.
