Exact Response Theory and Kuramoto dynamics

The dynamics of Kuramoto oscillators is investigated in terms of the ex- act 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.