  How much free energy is irreversibly lost during a thermodynamic process? For
deterministic protocols, lower bounds on energy dissipation arise from the
thermodynamic friction associated with pushing a system out of equilibrium in
finite time. Recent work has also bounded the cost of precisely moving a single
degree of freedom. Using stochastic thermodynamics, we compute the total energy
cost of an autonomously controlled system by considering both thermodynamic
friction and the entropic cost of precisely directing a single control
parameter. Our result suggests a challenge to the usual understanding of the
adiabatic limit: here, even infinitely slow protocols are energetically
irreversible.
