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Nonlinear Projection for Ballistic Correlation Functions: a Formula in Terms of Minimal Connected Covers
1Department of Mathematics, King's College London, Strand, London, WC2R 2LS UK.
Journal of Statistical Physics
|August 1, 2026
Summary
We developed a nonlinear projection formula for many-body systems. This formula relates correlation functions of observables to conserved densities, applicable in all dimensions and out of equilibrium.
Area of Science:
- Statistical Mechanics
- Many-Body Physics
- Nonlinear Dynamics
Background:
- Macroscopic dynamics in many-body systems are governed by conserved quantities.
- Ballistic Macroscopic Fluctuation Theory (BMT) formalizes this via local relaxation.
- Existing methods often rely on linear approximations or equilibrium assumptions.
Purpose of the Study:
- To derive a general nonlinear projection formula for correlation functions.
- To express these functions in terms of conserved densities.
- To extend applicability beyond linear response and equilibrium conditions.
Main Methods:
- Utilizing the Ballistic Macroscopic Fluctuation Theory.
- Applying Malyshev's formula for cumulant expansion.
- Developing a nonlinear projection based on minimal connected covers.
Main Results:
- A projection formula for n-point connected correlation functions (cumulants).
- The formula expresses correlations of local observables via those of conserved densities.
- General explicit formulas for two- and three-point functions in stationary states.
Conclusions:
- The derived nonlinear projection is valid in d >= 1 dimensions and out of equilibrium.
- It generalizes the linear-response principle to higher-order correlations.
- Provides a framework for analyzing complex dynamics using conserved quantities.
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