  One-dimensional Bose and Fermi gases with contact interactions are known to
exhibit the weak-strong duality, where the equilibrium thermodynamic properties
of one system at weak coupling are identical to those of the other system at
strong coupling. Here, we show that such duality extends beyond the
thermodynamics to the frequency-dependent complex bulk viscosity, which is
provided by the contact-contact response function. In particular, we confirm
that the bulk viscosities of the Bose and Fermi gases agree in the
high-temperature limit, where the systematic expansion in terms of fugacity is
available at arbitrary coupling. We also compute their bulk viscosities
perturbatively in the weak-coupling limit at arbitrary temperature, which via
the duality serve as those of the Fermi and Bose gases in the strong-coupling
limit.
