Field-Theoretic Derivation and Physical Realization of the Entropy Gradient Force in Cosmology

In this paper, I formally derive the Entropy Gradient Force (EGF) from a classical field-theoretic framework. Building on prior work in which EGF emerged from passive entropy asymmetries in a collisionless expanding medium, I show that this force arises naturally from a scalar potential field obeying a sourced Klein-Gordon-like equation. This formalism demonstrates that EGF is not a mathematical artifact, but a physically justified, conservative force that acts alongside gravity during the early stages of structure formation. The resulting model is short-ranged, time-dependent, and inherently tied to local entropy gradients