A Multi Affine Geometric Framework for Quantum Nonlocality. Unifying Berry Phases, Entanglement, and Coherence

Abstract: We develop a multi affine geometric framework to unify classical and quantum mechanical laws through the lens of information geometry. By combining the principle of stationary action with maximum entropy production, we show that divergences in dual affine connections naturally give rise to quantum interference and nonlocal correlations. These ideas of maximum entropy and stationary align with the framework of entropic dynamics, wherein time evolution emerges from information-theoretic principles. A key insight comes from Berry phases. the mismatch of multiple affine connections leads to a nontrivial holonomy or "area", explaining how Bell type inequalities can be violated up to the Tsirelson bound. Additionally, we interpret sharply peaked distributions as "pinning" or "sourcing" curvature in the information manifold, drawing an analogy to a membrane under uniform stress. In this view, entanglement and coherence emerge as geometric features, phases and rotations within an overarching multi affine structure. We conclude that phenomena such as wavefunction collapse and quantum steering can be viewed as constraints on the manifold's "laxity" or curvature, with far-reaching implications for understanding quantum behavior in a geometric-information setting.