Information-Capacity Saturation and Black-Hole Entropy: Constitutive Response and Higher-Derivative Diagnostics

We propose an information-capacity formulation of black-hole entropy in which the Bekenstein--Hawking entropy is interpreted as the saturation value of a coarse-grained information capacity associated with a horizon cross-section. For a stationary black hole in a two-derivative Einstein theory in D spacetime dimensions, we define{equation*}ₘₐₓ=A/4G_Dln 2, =/=4G_D/A,{equation*}where denotes the coarse-grained gravitational entropy and =A/(4GD). We propose that the maximally coarse-grained equilibrium branch satisfies =1. Remaining on this branch gives{equation*} A=4G_D\,,{equation*}which we interpret as a constitutive response relation rather than as an independent microscopic derivation of the area law. We test the organization against established black-hole results. At leading order, the five-dimensional D1--D5--P black hole satisfies{equation*}A_H/4G_5=2π√N_1N_5N_p,{equation*}matching the leading microscopic statistical entropy in the appropriate regime. We then generalize the construction to higher-derivative gravity by replacing the Bekenstein--Hawking entropy with the Wald entropy . As a literature benchmark, the subleading statistical entropy calculation of Castro and Murthy for the five-dimensional D1--D5--P system agrees with the Wald entropy of the corresponding R²-corrected supergravity theory. We reformulate this established matching as a saturation diagnostic without claiming a new microscopic derivation of the correction. As an explicit effective-theory calculation, we analyze a five-dimensional Einstein--Gauss--Bonnet black hole. We find that the ratio of Wald entropy to the Einstein area entropy is{equation*}/A_H/(4G_5)=1+{12αGB}{r_h^2},{equation*}while the corresponding differential entropy--area response is{equation*}/(A_H/4G_5)=1+{4αGB}{r_h^2}.{equation*}The Wald entropy also satisfies the first law M=TH for the solution considered. These results provide a concrete realization of the proposed information-capacity diagnostic. The main value of the framework is therefore organizational and diagnostic: it separates microscopic, coarse-grained, geometric, higher-derivative, and generalized entropies; introduces dimensionless occupancy variables; and provides mismatch parameters that can be tested independently. No microscopic derivation of universal information saturation is claimed. The proposal is instead presented as a constitutive hypothesis whose validity must be tested across independent gravitational and quantum-gravitational settings.