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Work fluctuation-dissipation trade-off in heat engines

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.