Physics of Knowing: A First-Principles Derivation from Information Mismatch to Balance Laws and Flow-Induced Geometry

Abstract

We develop a first-principles framework for the physics of knowing, derivingepistemic dynamics from information mismatch. Under minimal structuralassumptions, mismatch induces a quadratic energetic injection, leading toa balance law dE/dt = I - D that governs epistemic evolution. We show that the resulting imbalance field induces a minimal deformation ofthe affine connection on an augmented manifold, while the metric remains fixed.Thus, geometry is not imposed but emerges from imbalance-driven flow. At thermodynamic closure, imbalance vanishes and trajectories recover geodesicmotion. This provides a structural link between learning, thermodynamics,and geometry, and offers a new perspective in which dynamics arise intrinsicallyfrom information discrepancy rather than external optimization.