Suppression of work fluctuations by optimal control: An approach based on Jarzynski's equality

Abstract

Understanding and manipulating work fluctuations in microscale and nanoscale systems are of both fundamental and practical interest. For example, aspects of work fluctuations will be an important factor in designing nanoscale heat engines. In this work, an optimal control approach directly exploiting Jarzynski's equality is proposed to effectively suppress the fluctuations in the work statistics, for systems (initially at thermal equilibrium) subject to a work protocol but isolated from a bath during the protocol. The control strategy is to minimize the deviations of individual values of e^{-βW} from their ensemble average given by e^{-βΔF}, where W is the work, β is the inverse temperature, and ΔF is the free energy difference between two equilibrium states. It is further shown that even when the system Hamiltonian is not fully known, it is still possible to suppress work fluctuations through a feedback loop, by refining the control target function on the fly through Jarzynski's equality itself. Numerical experiments are based on linear and nonlinear parametric oscillators. Optimal control results for linear parametric oscillators are also benchmarked with early results based on shortcuts to adiabaticity.