Measurement is Dimensional Collapse: A Geometric Interpretation of Entropy

We propose a geometric interpretation of thermodynamic entropy grounded in measurement and dimensional projection. Rather than viewing entropy as disorder, missing information, or phase-space volume, we argue that entropy production fundamentally arises from the loss of structural information when high-dimensional system states are coarse-grained onto lower-dimensional measurement manifolds. This perspective resolves longstanding puzzles about ergodicity in macroscopic systems and provides a unified framework linking thermodynamics, information theory, and observer-dependent physics. We demonstrate that large systems are practically nonergodic due to exponential recurrence times, recast the Second Law as a dimensional collapse principle grounded in the data-processing inequality, and show that irreversibility emerges naturally from the one-way nature of coarse-graining. We predict that mesoscopic experiments preserving coherence in unmeasured dimensions will demonstrate sub-Landauer energy bounds. This framework has implications for reversible computation, biological thermodynamics, and the foundations of statistical mechanics.