The Universal Entropic Mass Principle: From Quantum Gaps to Cosmic Acceleration

The Universal Entropic Mass Principle (UEMP) postulates a minimum entropic cost {equation} Δ S ≥ {m c^2}{k_B Teff} {equation} for mass stabilization, generating a characteristic acceleration scale that reproduces the observed Radial Acceleration Relation (RAR) with performance comparable to MOND and lower AIC/BIC than NFW profiles, as shown in entropic galactic analyses by {Coutinho2026b} and tested against SPARC observations {SPARC2016}. The principle extends consistently to gravitational lenses, galaxy clusters, and cosmology, predicting a redshift-dependent limiting acceleration {equation} a_0(z) ∝ H(z), {equation} testable with upcoming large-scale surveys such as Euclid {Euclid_Lensing_2024}. Dark energy emerges naturally as a cumulative entropic density {equation} ρₑₙₜ ~ ∑_i m_i c^2/V T_i, {equation} producing repulsive pressure without invoking exotic fields or a cosmological constant, as derived theoretically in {Coutinho2026} and constrained by Planck observations {Planck2018Legacy}. The model predicts continuous accelerated expansion and monotonic entropy growth, even during cosmic cooling and in black-hole-dominated eras.