The dissipation-time uncertainty relation

We show that the entropy production rate bounds the instantaneous rate at which any process can be performed in stochastic systems. This implies a time-dissipation uncertainty relation $\langle \dot S_\text{e} \rangle \mathcal{T} \geq k_{\text{B}} $ for rare processes, in which the inverse rate is the mean time $\mathcal{T}$ to complete the process and the entropy production rate reduces to the constant entropy flow $\langle \dot S_\text{e} \rangle$ into the reservoirs. This is a novel form of classical speed limit: the smaller the dissipation, the larger the time to perform a process.