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Dissipation bounds the amplification of transition rates far from equilibrium

Benjamin Kuznets-Speck,David T. Limmer

Published 2020 in Proceedings of the National Academy of Sciences of the United States of America

ABSTRACT

Significance The speed of a dynamical transition is central to processes across the physical sciences, but general principles to predict and design transition rates within a nonequilibrium system remain elusive. With stochastic thermodynamics, we derive exact relations and inequalities for the ratio of transition rates at and away from thermal equilibrium. We show that excess energy dissipation during the transition imposes an upper limit on the possible speed-up. Amplifying a rate requires a minimum energetic cost—the larger the dissipation, the higher the possible rate amplification. We demonstrate this variational relation on diffusive barrier crossings driven by noisy and deterministic external forces and discuss how it can be leveraged to design optimal protocols for controlling rates in complex random systems. Complex systems can convert energy imparted by nonequilibrium forces to regulate how quickly they transition between long-lived states. While such behavior is ubiquitous in natural and synthetic systems, currently there is no general framework to relate the enhancement of a transition rate to the energy dissipated or to bound the enhancement achievable for a given energy expenditure. We employ recent advances in stochastic thermodynamics to build such a framework, which can be used to gain mechanistic insight into transitions far from equilibrium. We show that under general conditions, there is a basic speed limit relating the typical excess heat dissipated throughout a transition and the rate amplification achievable. We illustrate this tradeoff in canonical examples of diffusive barrier crossings in systems driven with autonomous and deterministic external forcing protocols. In both cases, we find that our speed limit tightly constrains the rate enhancement.

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