Holographic graphene response from generalized-entropy Smarr residual

Abstract We develop a fixed-geometry entropy-layer framework for testing generalized black-hole entropies beyond local thermodynamic consistency. Holding the seed spacetime, conserved charges, surface gravity, mass normalization, and Smarr weights fixed, we show that every smooth entropy representation generates an exact first-law response sector, while only selected deformation labels qualify as genuine Smarr-Euler work coordinates. The decisive object is a transported Smarr residual: scalar-closed and vector-closed sectors carry a state-independent Euler completion, whereas scale-memory sectors retain a branch-dependent entropy-scale fingerprint. Applying this criterion to standard generalized entropies, we find scalar closure for Rényi and canonical Kaniadakis sectors, vector closure for Sharma-Mittal entropy, and scale-memory behavior for Barrow, Tsallis-Cirto, logarithmic, generic Abe, and generic Hanel-Thurner representatives. Charged anti-de Sitter and BTZ finite-screen geometries provide analytic response laboratories for the residual. We then map the same residual structure into holographic graphene response, where entropy-sector memory appears as calibrated scaling drift in nanoribbon plasmon linewidths, optical response, quantum capacitance, compressibility, and Dirac-fluid transport. The resulting protocol turns generalized black-hole entropy deformations into falsifiable holographic fingerprints in graphene spectroscopy.