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arXiv · 2507.07600

The equilibrium distribution function for strongly nonlinear systems

Jialin Zhang·Yong Zhang·Hong Zhao
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Abstract

The equilibrium distribution function determines macroscopic observables in statistical physics. While conventional methods correct equilibrium distributions in weakly nonlinear or near-integrable systems, they fail in strongly nonlinear regimes. We develop a framework to get the equilibrium distributions and dispersion relations in strongly nonlinear many-body systems, incorporating corrections beyond the random phase approximation and capturing intrinsic nonlinear effects. The theory is verified on the nonlinear Schrodinger equation, the Majda-McLaughlin-Tabak model, and the FPUT-beta model, demonstrating its accuracy across distinct types of nonlinear systems. Numerical results show substantial improvements over existing approaches, even in strong nonlinear regimes. This work establishes a theoretical foundation for equilibrium statistical properties in strongly nonlinear systems.

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Jialin Zhang, Yong Zhang, Hong Zhao. 2025-07-10. The equilibrium distribution function for strongly nonlinear systems. https://arxiv.org/abs/2507.07600

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