Merits and Qualms of Work Fluctuations in Classical Fluctuation Theorems

TL;DR

This paper investigates how classical Hamiltonian chaos influences work fluctuations in nonequilibrium thermodynamics, revealing that adiabatic protocols minimize fluctuations and exploring implications for free energy calculations.

Contribution

It provides a general analysis of the impact of Hamiltonian chaos on work fluctuations and the divergence of variance in exponential work terms in classical systems.

Findings

Work fluctuations are minimized in adiabatic protocols for chaotic systems.

Divergence of variance in exponential work terms indicates universal behavior across protocols.

Insights inform the design of efficient work protocols in nanoscale thermodynamics.

Abstract

Work is one of the most basic notion in statistical mechanics, with work fluctuation theorems being one central topic in nanoscale thermodynamics. With Hamiltonian chaos commonly thought to provide a foundation for classical statistical mechanics, here we present general salient results regarding how (classical) Hamiltonian chaos generically impacts on nonequilibrium work fluctuations. For isolated chaotic systems prepared with a microcanonical distribution, work fluctuations are minimized and vanish altogether in adiabatic work protocols. For isolated chaotic systems prepared at an initial canonical distribution at inverse temperature $\beta$, work fluctuations depicted by the variance of $e^{-\beta W}$ are also minimized by adiabatic work protocols. This general result indicates that if the variance of $e^{-\beta W}$ diverges for an adiabatic work protocol, then it diverges for all nonadiabatic work protocols sharing the same initial and final Hamiltonians. How such divergence explicitly impacts on the efficiency of using the Jarzynski's equality to simulate free energy differences is studied in a Sinai model. Our general insights shall boost studies in nanoscale thermodynamics and are of fundamental importance in designing useful work protocols.