Status: Embargoed / Pre-Registration

Protocol #1: The Thermodynamics of Market Fragility

A Dissipative Systems Approach to Diagnosing Metastability in Financial Microstructure.

Principal Investigator: Dave Anaya
Date: Jan 2026 · Classification: Type I/II Phase Transitions

Abstract

Standard risk models, predicated on Geometric Brownian Motion (GBM), treat market crashes as exogenous "tail events" (3-sigma outliers). We propose an alternative hypothesis: extreme market events are endogenous phase transitions resulting from the accumulation of structural stress in a finite-rate open system.

This study introduces a diagnostic framework that maps market microstructure to a dimensionless thermodynamic state. We define a dimensionless stress density (H_eff), representing the Signal-to-Noise Ratio (SNR) of market stress relative to the thermal background.

By comparing this stress density against a dynamic critical capacity (H_c), we demonstrate that "crashes" are mechanistically distinct from "corrections." The former represents a first-order phase transition (viscosity collapse), resulting from the evaporation of the active hedging core. The latter represents a second-order transition (continuous relaxation), where the structure releases energy via volatility while retaining state integrity.

Methodology Snapshot

The Instability Index (Λ) is derived from the ratio of systemic stress density to critical capacity. The model integrates the visible limit order lattice (Nasdaq TotalView-ITCH) and a dynamic viscosity term derived from the thermodynamic state of the options market (OPRA).

[ MATHEMATICAL SPECIFICATION REDACTED ]

Pending OSF Registration and Peer Review

H_eff(t) = 1/Theta(t) * [ 1/2 kappa(t) (Z_P)^2 + 1/2 mu(t) (Z_Phi)^2 ]

Lambda = H_eff / H_critical

Figure 1: The Effective Hamiltonian of the Market State

We validate this using a saturation-based model of order book rigidity, a solvency-based boundary condition derived from a Naïve Merton structural model, and a dynamic capacity model that integrates the visible limit order lattice.

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The complete protocol, including the derivation of the Critical Capacity (H_c), is available to qualified research partners.

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Suggested Citation: Anaya, D. (2026). The Thermodynamics of Market Fragility. CatInCloud Labs. Protocol #1 (Embargoed).