Monetary Entropy and the Epistemic Limits of Economic Coordination: An Information-Theoretic Analysis

Abstract

This paper presents the FAURAS (Formal Analytical Unified Restriction on Access to Simultaneity) framework, which demonstrates how informational entropy creates fundamental epistemic barriers to economic coordination by imposing intrinsic limits on the simultaneous processing and aggregation of dispersed information necessary for market clearing. We provide mathematically rigorous definitions of monetary entropy based on volatility distributions, deriving the entropy-cognitive capacity relationship from information-theoretic principles. Complete formal verification in the Lean 4 proof assistant ensures mathematical soundness. Our theoretical framework proves that general equilibrium becomes epistemically unattainable when entropy exceeds critical thresholds. These thresholds are determined by system complexity. Using entropy measures applied to comprehensive daily financial market data (2000–2023; n = 8,309 daily observations), we validate theoretical predictions through multidimensional entropy analysis, capturing sectoral dispersion, yield curve dynamics and stress indicator alignment. The framework provides enhanced empirical support for theoretically grounded thresholds at H* = 0.5×ln(M) and H** = ln(M), where M represents market complexity. Our optimal entropy combination achieves predictive power for market stress with Granger-causal relationships extending 1-5 days ahead (p<0.001). The cognitive capacity degradation follows K(t)=C·e^(-λH(t)), where λ=ln(2)/H_critical, providing a precise quantification of limitations in information processing with formal proofs establishing monotonicity, impossibility conditions, and critical threshold properties. These findings establish entropy monitoring as a scientifically grounded tool for systemic risk assessment, with immediate applications in central bank communication strategies and financial stability policy.