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

TL;DR

This paper introduces an optimal control method leveraging Jarzynski's equality to suppress work fluctuations in microscale systems, enhancing the design of nanoscale heat engines and enabling fluctuation control even with incomplete system information.

Contribution

It proposes a novel optimal control approach based on Jarzynski's equality to reduce work fluctuations, including a feedback mechanism for systems with unknown Hamiltonians.

Findings

Effective suppression of work fluctuations demonstrated in numerical experiments.

Control strategy works even with partial knowledge of the system Hamiltonian.

Benchmarking shows improved performance over traditional adiabatic methods.

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 exp(-\beta W) from their ensemble average given by exp(-\beta \Delta F}, where W is the work, \beta\ is the inverse temperature, and \Delta F 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 accelerated adiabatic processes.