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 $⟨{\dot{S}}_{\text{e}}⟩\mathcal{T}\ge k_{\text{B}}$ between the entropy flow $⟨{\dot{S}}_{\text{e}}⟩$ 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.

Supplemented by detailed derivations

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