Thermofluid-inspired Nonlinear Entropy Model of Financial Markets with Time-varying External Shocks

Abstract

This study develops a thermofluid-inspired nonlinear entropy model to investigate uncertainty, instability, and risk propagation in financial markets under time-varying external shocks. The model is formulated as a nonlinear reaction–diffusion equation incorporating logistic-type growth, saturation effects, and a space–time-dependent source term representing decaying market disturbances. Through nondimensionalization, key governing parameters associated with diffusion, amplification, and dissipation are identified. Numerical solutions, obtained using an explicit finite difference scheme, reveal that increased diffusion enhances the spatial redistribution of financial entropy, thereby reducing localized instability. Nonlinear saturation limits excessive entropy growth, ensuring bounded system behavior, while external shocks significantly elevate entropy in the short term but exhibit diminishing long-term influence. Furthermore, entropy is shown to attain peak values at intermediate market depth and liquidity levels, highlighting a nonlinear balance between information flow and market friction. The results demonstrate that financial entropy dynamics are governed by the interplay of diffusion, nonlinear reactions, and transient shocks. The proposed framework provides a thermodynamically consistent and quantitatively robust approach for modeling market complexity, with potential applications in risk assessment, volatility prediction, and financial system stabilization.