Linguistic Thermodynamics: Calculating the 'Entropic Density' of Various Language Systems A Comparative Mathematical Analysis of Natural Languages and Artificial Codes

This paper introduces the framework of Linguistic Thermodynamics within the Acta Universi (AU) theoretical paradigm, proposing a mathematical model to calculate the 'entropic density' (ρ_S) and syntactic coherence (C_lang) of various language systems. Moving beyond classical Shannon information theory—which evaluates messages primarily as probabilistic symbol sequences independent of physical substrate or cognitive friction—the AU framework posits that text generation and code compilation represent physical-informational processes registering primary thought-forms onto the universal ledger (AU-log).We formulate an integral equation for entropic density (ρ_S) that incorporates lexical volume (V_lex), morphological valence (M_v), syntactic tree depth (D_tree), and higher-order structural constraints (N_gram). Through a comparative mathematical analysis, we evaluate three primary linguistic clusters: natural languages (inflective/synthetic, analytic, ideographic), regularized constructed languages (Esperanto), and formal programming languages (Python, C++).Our findings demonstrate that formal codes maximize syntactic coherence (C_lang → 1), minimizing execution friction for processors while concentrating entropic dissipation (ΔS_Θ) at the authoring phase; natural languages balance cognitive economy and expressive flexibility through dynamic morphological valence and structural redundancy; and constructed regularized languages achieve an engineered optimum, minimizing cross-lingual translation entropy penalties.