Harnessing Measurement Error as a Thermodynamic Resource in Two-Reservoir Information Engines

Abstract

In general, measurement error constrains the performance of information engines. However, this may not hold universally. In this work, we propose a class of two-reservoirs information engines (TRIEs) with a two-level system and demonstrate that the monotonic relationships between the work output, the efficiency, as well as the work fluctuations of the TRIEs and measurement error are determined by the demon's control parameters. Utilizing this, we establish the conditions that allow the TRIEs to generate useful work under any level of measurement error, and identify the regimes in which these performance parameters can be optimized simultaneously by the measurement error. Furthermore, we demonstrate that when the demon's energy cost is supplied solely by the cold reservoir, the efficiency that accounts for this cost can surpass the standard Carnot bound without violating the second law. Finally, we design a dual Otto cycles TRIE and provide an experimental scheme for its implementation based on a trapped $^{40}\mathrm{Ca}^+$ ion. Significantly, our results can be applied to the multi-level system information engines.