Dynamic Closure Theory for High-Frequency Market Microstructure

This work extends Dynamic Closure Theory (DCT), originally developed for turbulence and protein folding, to high-frequency financial market microstructure. The central idea is to treat local realised volatility as a driving “source” field and order-book liquidity depth as a bounded “coherence” field that quantifies how organised or resilient a limit order book is at any moment in time. From a maximum-entropy argument and a generic boundedness requirement, the framework yields a logistic closure equation for coherence and a simple power-law relation linking the source and coherence fields. Under a lognormal-style description of the volatility source, this architecture produces three concrete, parameter-free predictions for the statistical behaviour of the coherence field, which together define a falsifiable signature of order-book criticality. The paper does not claim that existing empirical studies have already confirmed these specific numerical values; instead, it uses the market microstructure literature only to check that the structural assumptions and directional predictions are compatible with known stylised facts, such as volatility clustering, heavy tails, and the tendency of liquidity depth to decline in turbulent markets. A minimal protocol is proposed for testing the theory on public limit-order-book datasets (for example, LOBSTER, FI-2010, and major cryptocurrency markets), but empirical results are left to future work.