Stronger Second-law-like Inequalities Implying Advantage of Feedback Control over Memory Cost

We report second-law-like inequalities (SLLIs) implying that feedback control increases maximum work more than compensates memory cost. Our SLLIs are stronger bounds than the second law (SLT) and the previous SLLIs that incorporate the correlations of a memory. The previous SLLIs claim that the memory's correlation increases the maximum work, but it is canceled out by memory cost. In contrast, our SLLIs reveal that when the subsystems of a controlled system internally correlate, the maximum work by open-loop control can be less than the feedback control, and this advantage of the feedback control can grow linearly with the system size under keeping the memory cost constant.