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Universal bounds on the performance of information-thermodynamic engine

We investigate fundamental limits on the performance of information processing systems from the perspective of information thermodynamics. We first extend the thermodynamic uncertainty relation (TUR) to a subsystem. Specifically, for a bipartite composite system consisting of a system of interest X and an auxiliary system Y, we show that the relative fluctuation of an arbitrary current for X is lower bounded not only by the entropy production associated with X but also by the information flow between X and Y. As a direct consequence of this bipartite TUR, we prove universal trade-off relations between the output power and efficiency of an information-thermodynamic engine in the fast relaxation limit of the auxiliary system. In this limit, we further show that the Gallavotti-Cohen symmetry is satisfied even in the presence of information flow. This symmetry leads to universal relations between the fluctuations of information flow and entropy production in the linear response regime. We illustrate these results with simple examples: coupled quantum dots and coupled linear overdamped Langevin equations. Interestingly, in the latter case, the equality of the bipartite TUR is achieved even far from equilibrium, which is a very different property from the standard TUR. Our results will be applicable to a wide range of systems, including biological systems, and thus provide insight into the design principles of biological systems.