Nonequilibrium Ensemble Averages Using Nonlinear Response Relations

Abstract

Abstract The transient time correlation function (TTCF) method is widely used in fluids and many-body systems to compute nonequilibrium transport quantities, providing improved signal-to-noise ratios in ensemble averages without requiring prohibitively large sample sizes. In spite of its success, the method has not been systematically explored for more general nonequilibrium 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 present novel derivations of the TTCF based on functional analytical approaches as well as on Markov chains. We discuss its relation to the spectral theory of stochastic systems, highlighting regimes where linear theory is insufficient and the TTCF gives response estimates with enhanced signal-to-noise ratios. 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.