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The dynamics of Kuramoto oscillators is investigated in terms of the exactresponse theory based on the Dissipation Function, which has been introduced inthe field of nonequilibrium molecular dynamics. While linear response theory isa cornerstone of nonequilibrium statistical mechanics, it does not apply, ingeneral, to systems undergoing phase transitions. Indeed, even a smallperturbation may in that case result in a large modification of the state. Anexact theory is instead expected to handle such situations. The Kuramotodynamics, which undergoes synchronization transitions, is thus investigated asa testbed for the exact theory mentioned above. A comparison between the twoapproaches shows how the linear theory fails, while the exact theory yields thecorrect response.

Exact Response Theory and Kuramoto dynamics