  We examine the effects of the Dzyaloshinsky-Moriya (DM) interaction on the
nonequilibrium thermodynamics in an anisotropic $XY$ spin chain, which is
driven out of equilibrium by a sudden quench of the control parameter of the
Hamiltonian. By analytically evaluating the statistical properties of the work
distribution and the irreversible entropy production, we investigate the
influences of the DM interaction on the nonequilibrium thermodynamics of the
system with different parameters at various temperatures. We find that
depending on the anisotropy of the system and the temperature, the DM
interaction may have different impacts on the nonequilibrium thermodynamics.
Interestingly, the critical line induced by the DM interaction can be revealed
via the properties of the nonequilibrium thermodynamics. In addition, our
results suggest that the strength of the DM interaction can be detected
experimentally by studying the nonequilibrium thermodynamics.
