Entropy-Driven Cosmic Expansion: A Thermodynamic Extension of General Relativity with Fluid and Gradient Contributions

We develop a thermodynamic extension of General Relativity in which local entropy production and spatial entropy gradients contribute to cosmic expansion. Two complementary mechanisms are considered: (i) an entropic fluid with energy density ρent and pressure pent, and (ii) spatial entropy gradients generating an effective negative pressure. Both mechanisms extend the Einstein equations through a covariantly conserved energy-momentum tensor derived from a variational principle. The resulting dynamics naturally allow environment-dependent expansion rates. Regions with enhanced entropy production—such as cosmic voids—can exhibit accelerated expansion, while dense regions expand more slowly. We examine the thermodynamic consistency of the energy exchange, provide a horizon-thermodynamic interpretation of the effective temperature, and present a quantitative estimate showing that a small entropic contribution in voids is sufficient to reproduce the observed Hubble tension. A first-order linear perturbation analysis demonstrates that the local Hubble parameter H(xμ) formally arises from the perturbed Einstein equations. The model is phenomenological yet physically consistent and offers a foundation for future perturbative and data-driven investigations.