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.