  Reducing work fluctuation and dissipation in heat engines or, more generally,
information heat engines that perform feedback control is vital to maximize
their efficiency. The same problem arises when we attempt to maximize the
efficiency of a given thermodynamic task that undergoes nonequilibrium
processes for arbitrary initial and final states. We find that the most general
trade-off relation between work fluctuation and dissipation applicable to
arbitrary nonequilibrium processes is bounded from below by the information
distance characterizing how far the system is from thermal equilibrium. The
minimum amount of dissipation is found to be given in terms of the relative
entropy and the Renyi divergence, both of which quantify the information
distance between the state of the system and the canonical distribution. We
give an explicit protocol that achieves the fundamental lower bound of the
trade-off relation.
