Thermonance: A Theoretical Framework for Entropy-Based Early Warning in Financial Markets

This position paper introduces thermonance a theoretical programme that transplants the Karimov-Alekberli (KA) seismological early-warning framework 12, 13 into nancial market microstructure. The KA model detects critical transitions in stressed physical systems by tracking the Causal Entropic Response (CER): the rate at which system entropy deviates from its historical baseline. We formally dene a nancial analogue the nancial CER (fCer) in terms of order-ow imbalance entropy, volume entropy, and bidask spread entropy, and derive the structural isomorphism from seismological to nancial variables. To illustrate the framework's internal consistency prior to empirical validation, we present an enhanced Monte Carlo simulation (N = 2,190 trading-day equivalent periods; 15 injected crash events across three severity levels). The simulation yields AUC = 0.96 (simplied fCer) and AUC = 0.79 (derivative-based full fCer) at a 25 day lead time. We are explicit throughout that these gures are simulation results, not empirical ndings; they demonstrate mathematical self-consistency, not predictive validity on real markets. We discuss two formulations of fCer a simplied level-based approximation suitable for theoretical analysis and a derivative-based full formulation consistent with the original KA denition and recommend an adaptive exponential-decay baseline (λ-EWMA) in place of a xed rolling window. The theoretical framework is applied to three asset classes (cryptocurrencies, foreign exchange, equity indices). An empirical research agenda in three stages is outlined.