Traversable Wormholes Supported by Entropy-Inspired Effective Matter Sectors

Abstract

The entropic interpretation of gravity suggests that spacetime geometry may encode thermodynamic information associated with microscopic degrees of freedom. In this context, the entropy--geometry correspondence of Refs.[1,2] links modified Bekenstein--Hawking entropies to deformed black-hole geometries and effective anisotropic matter sectors. Motivated by this result, we test whether these entropy-induced density profiles can act as phenomenological sources for traversable wormholes. Here we use the density sector as the thermodynamic input for a Morris--Thorne reconstruction, thereby isolating the role of the entropy-induced radial profile. The radial pressure follows from a barotropic equation of state, $p_r=wρ$, while the remaining variables are determined by the wormhole field equations and anisotropic equilibrium. We analyze five entropy-inspired sectors: Barrow, Tsallis, Kaniadakis, logarithmic, and exponential. Barrow and Tsallis are algebraic negative-density sources; Kaniadakis and exponential profiles are localized; and the logarithmic sector admits negative-density and positive-density phantom-like regimes. In all regular configurations, radial null-energy-condition violation at the throat is tied to the flare-out condition, while the tangential null energy condition and the strong-energy-condition combination diagnose the anisotropic redistribution of exoticity. The TOV balance is sector dependent: in the Barrow and Kaniadakis branches, the gravitational and compensating pressure contributions can reverse their signs together while remaining balanced; the other branches retain a common sign pattern with different degrees of near-throat localization. This framework shows that modified entropy profiles can provide viable effective sources for traversable wormholes, with the supporting mechanism depending sensitively on the underlying entropy deformation.