  We extend the well-known static duality \cite{girardeau1960relationship,
cheon1999fermion} between 1-D Bosons and 1-D Fermions to the dynamical version.
By utilizing this dynamical duality we find the duality of non-equilibrium work
distributions between interacting 1-D bosonic (Lieb-Liniger model) and 1-D
fermionic (Cheon-Shigehara model) systems with dual contact interactions. As a
special case, the work distribution of the Tonks-Girardeau (TG) gas is
identical to that of 1-D free fermionic system even though their momentum
distributions are significantly different. In the classical limit, the work
distributions of Lieb-Liniger models (Cheon-Shigehara models) with arbitrary
coupling strength converge to that of the 1-D noninteracting distinguishable
particles, although their elemetary excitations (quasi-particles) obey
different statistics, e.g. the Bose-Einstein, the Fermi-Dirac and the
fractional statistics. We also present numerical results of the work
distributions of Lieb-Liniger model with various coupling strengths, which
demonstrate the convergence of work distributions in the classical limit.
