Brownian Motion, Degrees of Freedom, and Entropy: A Structure-First Interpretation

Brownian motion is traditionally treated as an emergent stochastic phenomenon arising from microscopic collisions and thermal agitation. In this work, we present a structure-first reinterpretation in which Brownian motion is identified as the dynamical signature of under-constrained systems with high accessible degrees of freedom. Rather than representing fundamental randomness, diffusive behavior reflects the absence of structural constraints capable of suppressing or channeling motion into stable pathways. Within this framework, entropy functions as a descriptive measure of unconstrained accessibility rather than a causal driver of dynamics. This interpretation complements constraint-dominated regimes such as nodal persistence and gravitational confinement, providing a unified classification of physical behavior across low- and high-constraint domains without modifying established statistical mechanics.