Thermodynamics of Internal Correlations

Earlier studies have revealed that Maxwell's demon must obey the second law of thermodynamics. However, it is still an open question whether there is a fundamental net gain and indispensability of using information. Here, gain refers to free energy or mechanical work. In this paper, we report a novel generalization of the second law of thermodynamics that answers this question in affirmative. The entropy production can be split into two contributions: the entropy productions of the individual subsystems and the decrease in the correlations internally between subsystems. Our novel generalization of the second law implies that information is indispensable and that a positive net gain can be realized if an agent exploits the latter contribution of this split. Particularly, it is shown that the total entropy production has a lower bound corresponding to the positive quantity that emerges when the internal correlations of the target system diminish without the correlation between an agent and the target of its control. In other words, the target information is indispensable for exploiting the internal correlations to extract free energy or work. As the internal correlations can grow linearly with the number of the subsystems constituting the target system, the control with such correlations, i.e., feedback control, can provide substantial gain that exceeds the operational cost paid for performing the feedback control, which is negligible in the thermodynamic limit. Thus, the generalized second law presented in this paper can be interpreted as a physical principle that explains the mechanism through which information becomes not only substantially beneficial and but also inevitable at the macroscopic scale.