Fluctuation-response relations for multitime correlations

Area of Science:

• Statistical physics
• Dynamical systems theory
• Computational physics

Background:

• Calculating time-correlation functions is crucial for understanding statistical dynamical systems.
• Existing methods can be computationally intensive or limited in scope.
• The relationship between fluctuations and responses is a key concept in non-equilibrium physics.

Purpose of the Study:

• To establish a general method for calculating arbitrary-order time-correlation functions in statistical dynamical systems.
• To demonstrate that these correlations can be computed as higher-order response functions.
• To explore the implications for moment closure approximations and computational strategies.

Main Methods:

• Derivation of fluctuation-response relations based on a variational characterization of the generating functional.
• Extension of these relations to moment closure approximations using the Rayleigh-Ritz procedure.
• Analysis of higher-order correlations, including nonlinear effects from fluctuation interactions.

Main Results:

• Arbitrary-order time correlations can be calculated as higher-order response functions to a modified master equation.
• Fluctuation-response relations are preserved in variational Rayleigh-Ritz moment closures.
• For higher-order correlations, dynamical generation by nonlinear fluctuation interactions is identified.

Conclusions:

• The developed fluctuation-response relations offer a powerful new tool for analyzing statistical dynamical systems.
• These relations simplify the computation of time correlations, particularly with automatic differentiation.
• The findings have direct applications in areas like turbulent energy decay modeling.