Entropy Without Microstates

Arc I — Accessibility Paper 5 Title Entropy Without Microstates Zenodo DOI 10.5281/zenodo.18180810 Description This paper develops a formulation of entropy that does not rely on microscopic degrees of freedom, statistical ensembles, or underlying state-counting assumptions. Instead, entropy is defined operationally as a measure of inaccessible correlation: the irrecoverable loss of distinguishability imposed by finite accessibility. The analysis shows that entropy arises whenever observational channels degrade correlations beyond recovery, independent of whether an underlying microstate description exists. Classical thermodynamic entropy, horizon entropy, and information-theoretic entropy are unified as special cases of accessibility collapse under different physical constraints. By removing microstates from the foundation of entropy, the paper resolves long-standing conceptual tensions between thermodynamics, gravity, and quantum information. Entropy increase is reinterpreted as a directional loss of operational resolution rather than as an increase in hidden microscopic complexity. This accessibility-based entropy naturally accommodates horizon entropy, coarse-graining, and irreversibility without invoking ergodicity, equilibrium, or statistical mechanics. It provides the conceptual bridge between causal limitations (Arc I) and emergent thermodynamic behavior (Arc II). Keywords entropy; irreversibility; information loss; accessibility collapse; non-statistical thermodynamics; horizons Notes Arc I — Accessibility (conceptual capstone) Entropy defined without microstates or ensembles Unifies thermodynamic and horizon entropy Resolves entropy–gravity–information tensions Direct precursor to thermalization and measurement arcs