Thermodynamics of Internal Correlations

Earlier studies revealed that Maxwell's demon must obey the second law of thermodynamics. However, the presence of a physical principle explaining whether using information is profitable and inevitable remains uncertain. This paper reports a novel generalization of the second law of thermodynamics, answering whether such a physical principle exists in the affirmative. The entropy production can be split into two contributions: the entropy production of the individual subsystems and the reduction in the correlations between subsystems. This novel generalization of the second law implies that if an agent exploits the latter factor, then information is indispensable and provides free energy or mechanical work outweighing the operational cost. In particular, the total entropy production has a lower bound corresponding to the positive quantity that emerges when the internal correlations of the controlled target diminish, but the correlations between the agent and target do not exist. Therefore, the information about the target is indispensable for exploiting the internal correlations to extract free energy or work. Furthermore, as the internal correlations can grow linearly with the number of the subsystems constituting the target system, control with such correlations, i.e., feedback control, can yield substantial gain that exceeds the operational cost of performing 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 ensures the benefit and inevitability of information processing.