The dissipation-time uncertainty relation

Abstract: We show that the dissipation rate bounds the rate at which physical processes can be performed in stochastic systems far from equilibrium. Namely, for rare processes we prove the fundamental tradeoff $\langle \dot S_\text{e} \rangle \mathcal{T} \geq k_{\text{B}} $ between the entropy flow $\langle \dot S_\text{e} \rangle$ into the reservoirs and the mean time $\mathcal{T}$ to complete a process. This dissipation-time uncertainty relation is a novel form of speed limit: the smaller the dissipation, the larger the time to perform a process.