ENTROPIX: A Comprehensive Basis for R&D for a Unification Candidate Based on Irreversible Quantum Information Flows

This white paper introduces ENTROPIX, a hierarchical entropy monotonicity unificationframework that reinterprets low-energy physics as emergent attractors from irreversible quantum information flows in open systems. Synthesizing updated research programs DimensionalMeasurement Equilibrium (DME), ENTROPIA (with Fisher metric and slave equations), andEntropic Damping Force (EDF), ENTROPIX positions entropy as the foundational organizingprinciple, deriving features consistent with General Relativity (GR) and the Standard Model(SM) without new particles or fine tuning.Two master conditions stationary coarse-grained information flow and non-decreasing entropy export select stable configurations as entropy-optimal attractors. Centered on a recursively nested compounded-exponential benchmark, proven variationally optimal via EulerLagrange equations, ENTROPIX derives: (1) dimensional stability at D = 4 from unitarityconstraints with S(ϵ) ≈ S0(1 − 0.703ϵ2), (2) non Abelian gauge structures from tripartite entropy maximization, (3) exactly three fermion generations from inflection point counting, (4)flavor hierarchies consistent with experimental Yukawa matrices, and (5) emergent gravity consistent with Jacobson’s thermodynamic derivation. ENTROPIX advances as a comprehensive emergent candidate resolving cosmological tensions (including the H0 and S8 discrepancies) while aligning with empirical minimalism andBayesian model selection principles