Exact Response Theory and Kuramoto dynamics

TL;DR

This paper applies an exact response theory based on the Dissipation Function to Kuramoto oscillator dynamics, demonstrating its effectiveness over linear response theory in systems with phase transitions like synchronization.

Contribution

It introduces an exact response framework for Kuramoto dynamics, addressing limitations of linear response theory in phase transition scenarios.

Findings

Exact response theory accurately predicts system behavior during synchronization transitions.

Linear response theory fails to capture large responses near phase transitions.

The study validates the exact theory as a robust tool for nonequilibrium systems with phase changes.

Abstract

The dynamics of Kuramoto oscillators is investigated in terms of the exact response theory based on the Dissipation Function, which has been introduced in the field of nonequilibrium molecular dynamics. While linear response theory is a cornerstone of nonequilibrium statistical mechanics, it does not apply, in general, to systems undergoing phase transitions. Indeed, even a small perturbation may in that case result in a large modification of the state. An exact theory is instead expected to handle such situations. The Kuramoto dynamics, which undergoes synchronization transitions, is thus investigated as a testbed for the exact theory mentioned above. A comparison between the two approaches shows how the linear theory fails, while the exact theory yields the correct response.