Work fluctuation and total entropy production in nonequilibrium processes

TL;DR

This paper explores the relationship between work fluctuation and entropy production in nonequilibrium thermodynamics, proposing optimal protocols to minimize entropy while controlling work fluctuations in small systems.

Contribution

It introduces a variational approach to find protocols that minimize total entropy production for a given work fluctuation in nonequilibrium processes starting from arbitrary states.

Findings

Derived a stationary solution for the trade-off relation.

Constructed explicit protocols combining adiabatic and quasi-static processes.

Showed how to suppress work fluctuation and entropy production simultaneously.

Abstract

Work fluctuation and total entropy production play crucial roles in small thermodynamic systems subject to large thermal fluctuations. We investigate a trade-off relation between them in a nonequilibrium situation in which a system starts from an arbitrary nonequilibrium state. We apply the variational method to study this problem and find a stationary solution against variations over protocols that describe the time dependence of the Hamiltonian of the system. Using the stationary solution, we find the minimum of the total entropy production for a given amount of work fluctuation. An explicit protocol that achieves this is constructed from an adiabatic process followed by a quasi-static process. The obtained results suggest how one can control the nonequilibrium dynamics of the system while suppressing its work fluctuation and total entropy production.