  Previous research has consistently affirmed that Maxwell's demon must adhere
to the second law of thermodynamics. Yet, the unresolved question remains
whether the profitability and indispensability of information, which we
routinely take for granted, are based on constraints stemming from physical
laws. This paper reports a novel generalization of the second law of
thermodynamics, answering that when internal correlations, i.e., correlations
between subsystems of resource, are intended to be exploited, information is
indispensable to extract free energy. Furthermore, the internal correlations,
which can grow linearly with the number of subsystems in the resource, allow
for control with information that yields significant gains, dwarfing the
negligible operational costs in the thermodynamic limit. Thus, the generalized
second law presented herein can be interpreted as a fundamental physical
principle that ensures the benefit and inevitability of information processing
in thermodynamics.
