International Journal For Multidisciplinary Research

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Beyond Equilibrium: Phase Transitions and the Statistical Mechanics of Financial Panics - A Quasi-Equilibrium Bethe-Peierls Approach to Econophysics

Author(s) Prof. Syed Azhara Yaqoob, Prof. Gowhar Hussain Bhat
Country India
Abstract This paper investigates financial market dynamics through the lens of statisti-cal physics, focusing on stock market crashes as phase transitions. Following the pioneering work of Gligor and Ignat [1], we develop a detailed mathematical frame-work using the Ising model in the Bethe-Peierls (quasi-chemical) approximation [2, 3] to model collective trader behaviour. We demonstrate that financial panics can be conceptualised as phase transitions in complex adaptive economic networks [4], where traders are represented as interacting spins on a lattice [5, 6]. Our model accounts for local correlations between traders while maintaining computational tractability, yielding a critical temperature, order parameters, and a specific heat that exhibit qualitative similarities to empirical financial data [7, 8]. We derive model-based indicators for market sentiment, herding intensity, crash propensity, and systemic risk. We emphasise that these indicators are theoretical con-structs; empirical calibration and out-of-sample validation remain open problems. The results provide a mathematical foundation for understanding col-lective trading behaviour and market instabilities, and move beyond the conceptual limitations of equilibrium economics. We also present a Glauber-type master equa-tion that embeds the equilibrium Bethe-Peierls solution as the stationary state of a stochastic relaxation dynamics, thereby clarifying the sense in which the model describes non-equilibrium behaviour.
Keywords Econophysics, Phase Transitions, Bethe-Peierls Approximation, Ising Model, Financial Crashes, Herding Behavior, Market Sentiment, Systemic Risk, Critical Phenom-ena, Statistical Physics, Complex Systems, Glauber Dynamics, Quasi-Equilibrium
Field Mathematics > Economy / Commerce
Published In Volume 8, Issue 5, September-October 2026
Published On 2026-10-13
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CrossRef DOI prefix of IJFMR is 10.36948/ijfmr

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