The Exergy of the Word: Recursive Divergence and the Thermodynamic Ceiling of Languages

This repository contains the paper, analysis scripts, simulation code, and data for a study of recursive divergence in semantic entropy. Using Classical Latin as a frozen baseline, decomposition trees for 12 modern concepts (depth 0 to 5) demonstrate that the cost of expressing a concept across a conceptual gap grows as C(d) = 7.8 × 1.94^d (R² = 0.93). Two regimes are identified: flat O(1) when sub-concepts are available, and recursive O(b^d) when the conceptual infrastructure is absent. An extended Abrams-Strogatz simulation shows that vocabulary depth accelerates language collapse by up to 85% at equal prestige. The unified equation C(d, A) = b^d × C₀(A) links conceptual depth and phonemic inventory size in a single expression for the lexical carrying capacity of a language.