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This preprint introduces a new theoretical framework proposing that entropy gradients—formed passively through velocity-based separation in a collisionless, expanding medium—can generate a conservative, time-dependent force. Rooted in a thought experiment involving time-gated particle escape, the framework demonstrates how purely kinematic sorting, without interactions, feedback, or measurements, can lead to spatial entropy asymmetries. These gradients, in turn, act as the source of a scalar potential field (termed the VEG field), whose negative gradient defines a short-ranged, Yukawa-like force: the VEE (Entropy Emergent) Force. The theory is developed mathematically through both a phenomenological Fourier-space entropy spectrum and a classical field-theoretic Lagrangian, leading to a sourced Klein–Gordon equation governing the entropy potential. Numerical simulations across multiple scenarios—free evolution, local entropy estimation, and gravitational coupling—confirm the spontaneous emergence and dynamic effects of the VEE force. The framework is further tested against observational data from GD-1, Draco, and Fornax, showing encouraging consistency without requiring fine-tuned parameters.