Geometric Amplification in Asymmetric Logarithmic Superpositions: A Theoretical Model of Phase Drift with Extensions to Open Quantum Systems

This work establishes a geometric law for systematic phase accumulation in finite asymmetric superpositions of complex exponentials xαk+iβkx^{\alpha_k + i\beta_k}x^{\alpha_k + i\beta_k} (x>1x > 1x > 1), with positive correlation between αk\alpha_k\alpha_ka nd βk\beta_k\beta_k. The main theorem proves a bias term amplified by a geometric factor of 2, arising from quadratic intensity weighting and directed branch-cut jumps.Rigorous extensions include effective error bounds, universality for arbitrary densities, generalizations to nonlinear correlations, a two-term illustrative model, a stochastic master equation interpretation, and a Gaussian limit providing probabilistic foundation. A formal analogy to phase damping in open quantum systems via the Lindblad equation is developed, where correlated jump rates yield an identical factor-2 amplification in decoherence bias.The framework provides a unified geometric perspective on asymmetry-induced drift in classical and quantum oscillatory sums.