  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.
