Finite-time thermodynamic bounds and trade-off 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 trade-off relations between incompatible information processing such as measurement and feedback in the finite-time regime. To this end, we introduce a general framework based on the concept of the Pareto front for thermodynamic costs, revealing the existence of fundamental trade-off relations between them. Focusing on discrete Markov jump processes, we consider the trade-off relation between thermodynamic activities, which in turn determines the trade-off relation between entropy productions. To identify the Pareto fronts, we introduce a new Wasserstein distance that captures the thermodynamic costs of subsystems, providing a geometrical perspective on their structure. Our framework enables us to find the optimal entropy production of subsystems and the optimal time evolution to realize it. 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 trade-off relation enables the realization of the demon. We also show that an optimal Maxwell's demon can be implemented by using double quantum dots. Furthermore, our framework is applicable to larger scale systems with multiple states, as demonstrated by a model of chemotaxis. Our results would serve as a designing principle of efficient thermodynamic machines performing information processing, from single electron devices to biochemical signal transduction.