Exact Response Theory and Kuramoto dynamics
arXiv:2108.09092 · doi:10.1016/j.physd.2021.133076
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.
References in corpus (16)
- Synchronization in complex networks
- Dynamical ensembles in stationary states
- Non equilibrium steady states: fluctuations and large deviations of the density and of the current
- Spontaneous synchrony in power-grid networks
- Fluctuation-Dissipation: Response Theory in Statistical Physics
- Nonequilibrium linear response for Markov dynamics, I: jump processes and overdamped diffusions
- On the Application of the Gallavotti-Cohen Fluctuation Relation to Thermostatted Steady States Near Equilibrium
- The Steady State Fluctuation Relation for the Dissipation Function
- A meaningful expansion around detailed balance
- Beyond the linear Fluctuation-Dissipation Theorem: the Role of Causality
- A diffusive system driven by a battery or by a smoothly varying field
- The mathematics of asymptotic stability in the Kuramoto model
- On the relaxation to nonequilibrium steady states
- Equilibrium, fluctuation relations and transport for irreversible deterministic dynamics
- Fluctuation-dissipation relation for chaotic non-Hamiltonian systems
- Elements of a unified framework for response formulae