Multidimensional measures of impulsively driven stochastic systems based on the Kullback-Leibler distance

TL;DR

This paper introduces multidimensional Kullback-Leibler response functions to analyze impulsively driven stochastic systems, revealing different dynamical information than traditional linear response functions, especially in overdamped systems.

Contribution

It defines and compares nonlinear Kullback-Leibler response functions with linear expectation-based functions for stochastic systems, highlighting their different informational content.

Findings

KLRF encode different dynamical information than ORF.

Two-dimensional KLRF shows distinct behavior depending on initial conditions.

KLRF variation with time delays differs between steady state and thermal equilibrium.

Abstract

By subjecting a dynamical system to a series of short pulses and varying several time delays we can obtain multidimensional characteristic measures of the system. Multidimensional Kullback-Leibler response function (KLRF), which are based on the Kullback-Leibler distance between the initial and final states, are defined. We compare the KLRF, which are nonlinear in the probability density, with ordinary response functions (ORF) obtained from the expectation value of a dynamical variable, which are linear. We show that the KLRF encode different level of information regarding the system's dynamics. For overdamped stochastic dynamics two dimensional KLRF shows a qualitatively different variation with the time delays between pulses, depending on whether the system is initially in a steady state, or in thermal equilibrium.