Fundamental Advantage of Feedback Control Based on a Generalized Second Law of Thermodynamics
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Based on a novel generalized second law of thermodynamics, we demonstrate that feedback control enjoys more net-extractable work than the control without measurements. The generalized second law asserts that the total entropy production of a closed system is bounded below by correlation's dissipation, simply named co-dissipation. Accordingly, co-dissipation is entropy production not to be converted to work. For the control without measurement, co-dissipation is caused by the loss of internal correlations among subsystems. On the other hand, because the feedback control can vanish the co-dissipation, it can extract work in principle from the internal correlation loss, which results in its fundamental advantage. Moreover, the characteristics of co-dissipation are consistent with heat dissipation in terms of irreversible useless entropy production. Hence, the generalized second law implies that the system's entropy production is bounded by the sum of two types of dissipation: heat and correlation. The generalized second law is derived by taking the sum of the entropy productions for all subsystems. We develop the technique for this computation, where the entropy productions are summed in parallel with the sequence of the graphs representing the dependency among subsystems. Furthermore, the positivity of co-dissipation is guaranteed by a purely information-theoretic fact, the data processing inequality, which will possibly shed light on the relation between thermodynamics and information theory.
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