  Complex systems can convert energy imparted by nonequilibrium forces to
regulate how quickly they transition between long lived states. While such
behavior is ubiquitous in natural and synthetic systems, currently there is no
general framework to relate the enhancement of a transition rate to the energy
dissipated, or to bound the enhancement achievable for a given energy
expenditure. We employ recent advances in statistical thermodynamics to build
such a framework, which can be used to gain mechanistic insight on transitions
far from equilibrium. We show that under general conditions, there is a basic
speed-limit relating the typical excess heat dissipated throughout a transition
and the rate amplification achievable. We illustrate this trade-off in
canonical examples of diffusive barrier crossings in systems driven with
autonomous and deterministic external forcing protocols. In both cases, we find
that our speed limit tightly constrains the rate enhancement.
