Finite-time thermodynamic bounds and tradeoff relations for information processing

In thermal environments, information processing requires thermodynamic costs determined by the second law of thermodynamics. Information processing within finite time is particularly important, since fast information processing has practical significance but is inevitably accompanied by additional dissipation. In this paper, we reveal the fundamental thermodynamic costs and the tradeoff relations between incompatible information processing such as measurement and feedback in the finite-time regime. To this end, we generalize optimal transport theory so as to be applicable to subsystems such as the memory and the engine in Maxwell's demon setups. Specifically, we propose a general framework to derive the Pareto fronts of entropy productions and thermodynamic activities, and provide a geometrical perspective on their structure. In an illustrative example, we find that even in situations where naive optimization of total dissipation cannot realize the function of Maxwell's demon, reduction of the dissipation in the feedback system according to the tradeoff relation enables the realization of the demon. We also show that an optimal Maxwell's demon can be implemented by using double quantum dots. Our results would serve as a designing principle of efficient thermodynamic machines performing information processing, from single electron devices to biochemical signal transduction.