  We study by using Monte Carlo simulations the hysteresis in unzipping and
rezipping of a double stranded DNA (dsDNA) by pulling its strands in opposite
directions in the fixed force ensemble. The force is increased, at a constant
rate from an initial value $g_0$ to some maximum value $g_m$ that lies above
the phase boundary and then decreased back again to $g_{0}$. We observed
hysteresis during a complete cycle of unzipping and rezipping. We obtained
probability distributions of work performed over a cycle of unzipping and
rezipping for various pulling rates. The mean of the distribution is found to
be close (the difference being within 10%, except for very fast pulling) to the
area of the hysteresis loop. We extract the equilibrium force versus separation
isotherm by using the work theorem on repeated non-equilibrium force
measurements. Our method is capable of reproducing the equilibrium and the
non-equilibrium force-separation isotherms for the spontaneous rezipping of
dsDNA.
