Dissipation-Time Uncertainty Relation

Abstract

We show that the entropy production rate bounds the rate at which physical processes can be performed in stochastic systems far from equilibrium. In particular, we prove the fundamental tradeoff $⟨{\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{S}}_{e}⟩\mathcal{T}\ensuremath{\ge}{k}_{B}$ between the entropy flow $⟨{\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{S}}_{e}⟩$ into the reservoirs and the mean time $\mathcal{T}$ to complete any process whose time-reversed is exponentially rarer. This dissipation-time uncertainty relation is a novel form of speed limit: the smaller the dissipation, the larger the time to perform a process.

Topics & Concepts