Nonequilibrium ensemble averages using nonlinear response relations

TL;DR

This paper explores the use of the transient time correlation function (TTCF) method for calculating nonlinear response functions in diverse non-equilibrium systems, extending its application beyond molecular fluids.

Contribution

It provides an analytical and numerical framework for applying TTCF to general non-equilibrium dynamical systems, including those with unknown invariant measures.

Findings

TTCF improves signal-to-noise ratios in ensemble averages.

The method is effective in systems far from equilibrium.

Relation to spectral theory enhances understanding of nonlinear responses.

Abstract

The transient time correlation function (TTCF) method is widely used in molecular fluids to compute non-equilibrium transport quantities, providing improved signal-to-noise ratios in ensemble averages without requiring prohibitively large sample sizes. In spite of its success in molecular and turbulent fluid systems, the method has not been systematically explored for more general non-equilibrium dynamical systems, including geophysical applications where the invariant measure is typically unknown. In this work, we present an analytical and numerical investigation of the TTCF method for computing nonlinear response functions in systems far from equilibrium. We discuss its relation to the spectral theory of stochastic systems, highlighting regimes where linear theory is insufficient and the advantages of TTCF. The aim of this work is to provide a framework for studying transient and steady-state responses using the TTCF approach in a broad class of nonequilibrium systems.