Stochastic control in microscopic nonequilibrium systems

¹ Department of Physics, Simon Fraser University - Burnaby, British Columbia, V5A 1S6, Canada
² Laboratoire J.A. Dieudonné, UMR CNRS 6621, Université de Nice Sophia- Antipolis - Nice 06108, France
³ Pacific Institute of Mathematical Sciences, UMI 3069 - Vancouver, British Columbia, Canada

Received: 2 October 2018
Accepted: 16 October 2018

Abstract

Quantifying energy flows at nanometer scales promises to guide future research in a variety of disciplines, from microscopic control and manipulation, to autonomously operating molecular machines. A general understanding of the thermodynamic costs of nonequilibrium processes would illuminate the design principles for energetically efficient microscopic machines. Considerable effort has gone into finding and classifying the deterministic control protocols that drive a system rapidly between states at minimum energetic cost. But when the nonequilibrium driving is imposed by a molecular machine that is itself strongly fluctuating, driving protocols are stochastic. Here we generalize a linear-response framework to incorporate such protocol variability and find a lower bound on the work that is realized at finite protocol duration, far from the quasistatic limit. Our findings are confirmed in model systems. This theory provides a thermodynamic rationale for rapid operation, independent of functional incentives.