Entropy as a Measure of the Number of Microstates, Not "Missing Information": Epistemic Analogy vs Ontological Property

This article analyses the widespread interpretation of entropy as “missing information” about the microstate of a system. It is shown that this interpretation, which derives from the formal similarity of the Boltzmann and Shannon formulas, is an epistemic analogy, not an ontological identity.

Three concepts are distinguished: Clausius thermodynamic entropy (a state function), Boltzmann–Gibbs statistical entropy ( S = k_B \ln \Omega ), and Shannon informational entropy (a measure of uncertainty). Entropy is a physical quantity, an objective property of the system, independent of any observer.

Drawing on the work of Schiffer (1991) and Alicki (2014), it is shown that entropy is not “information”, but merely defines the upper bound on the information that can be obtained about a system. Counter‑examples (equilibrium state, known configuration, collapsar entropy) demonstrate the independence of physical entropy from the observer’s knowledge.

The “missing information” interpretation is a useful heuristic, but its ontologisation is methodologically erroneous. The correct reformulation is: “Entropy is a physical quantity S = k_B \ln \Omega . The observer’s uncertainty is an epistemic state, not a property of the system.” The article is the fifth in the series “Reformulating Key Concepts of Physics Without Informational Language”.

Keywords: entropy, information, missing information, Boltzmann, Shannon, epistemic analogy.