  A generalized version of the Maximum Work Theorem is valid when the system is
initially not at thermal equilibrium. In this work, we initially study the
fraction of trajectories that violate this generalized theorem for a two simple
systems: a particle in a harmonic trap (i) whose centre is dragged with some
protocol, and (ii) whose stiffness constant changes as a function of time. We
also find the optimal protocol that minimizes the average change in total
entropy. To our surprise, we find that optimization of protocol does not
necessarily entail maximum violation fraction.
