Shaping rare events away from equilibrium: bounds on transition rate enhancement and a new take on optimal control of reaction rates.

Nonequilibrium forces often regulate how quickly a complex random system transitions between long-lived states, but there are few theories or guiding principles for how transition rates are enhanced by time-dependent external influence. Using tools from stochastic thermodynamics, we develop a general theory of rate enhancement in the transition path ensemble, leading to fundamental bounds on the ratio of transition rates. Under generic physical conditions, we show that the heat dissipated over the course of the transition sets an upper limit on achievable rate enhancement. This basic tradeoff between speed and energy consumption is illustrated in canonical examples of barrier crossing under autonomous, active, and periodically modulated driving protocols. We discuss how our bounds can be employed as a variational principle to design optimal protocols for tuning a system to achieve a target rate, and inferring rare reaction rates in (non)equilibrium settings.