Toward a Tripartite Taxonomy of Entropy in Physics

The term "entropy" denotes several mathematically distinct quantities across modern physics, including thermodynamic, statistical, quantum-informational, and geometric notions that are often conflated in foundational discussions. We propose an operational distinction among three such quantities: a geometric capacity entropy Scapacity proportional to a region's bounding area, a microscopic content entropy Scontent given by the fine-grained von Neumann entropy of the reduced state, and a thermodynamic entropy Sthermo corresponding to the observer-relative ignorance that remains after accessible information is accounted for. We argue that keeping these quantities distinct is not merely terminological: within this framework, the second law of thermodynamics can be formulated as a typical consequence of unitary dynamics combined with bounded observational access, rather than as an independent postulate. The distinction also clarifies which entropy enters established results such as the Bekenstein-Hawking entropy of black holes and the Clausius relation in Jacobson's thermodynamic derivation of Einstein's equations. The proposed framework is conceptual and does not modify established physical theories; it is intended as a useful clarification for informational approaches to physics.