Exact response theory and Kuramoto dynamics

@article{Amadori2021ExactRT,
  title={Exact response theory and Kuramoto dynamics},
  author={Debora Amadori and Matteo Colangeli and Astrid Correa and Lamberto Rondoni},
  journal={Physica D: Nonlinear Phenomena},
  year={2021}
}
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… 

Figures from this paper

References

SHOWING 1-10 OF 59 REFERENCES
A dynamical-systems interpretation of the dissipation function, T-mixing and their relation to thermodynamic relaxation
We review the notions of the dissipation function and T-mixing for non-invariant measures, recently introduced for nonequilibrium molecular dynamics models. We provide a dynamical-systems
‘A’
  • P. Alam
  • Composites Engineering: An A–Z Guide
  • 2021
Dissipation Function: Nonequilibrium
  • Physics and Dynamical Systems. Entropy,
  • 2020
Dissipation Function: Nonequilibrium Physics and Dynamical Systems
TLDR
The relation between linear and exact response is investigated, pointing out conditions for the validity of the response theory, as well as difficulties and opportunities for the physical interpretation of certain formal results.
Equilibrium.
Just as cellular imbalances on a microsopic level can have macroscopic consequences in systemic diseases, so one instrument playing out of tune in an orchestra can compromise the harmony of the
  • 2018
Statistical Physics of Synchronization
Statistical physics of synchronization. SpringerBriefs in Complexity
  • 2018
The mathematics of asymptotic stability in the Kuramoto model
TLDR
The mathematical results on asymptotic stability of stationary solutions in the continuum limit of the Kuramoto model are reviewed, insights into the principal arguments of proofs are provided, and possible extensions to some variations of the model are suggested.
Broken versus Non-Broken Time Reversal Symmetry: Irreversibility and Response
TLDR
It is shown that situations commonly assumed to violate the time reversal symmetry in reality do not violate this symmetry, and can be treated with standard theories and within standard experimental protocols.
...
1
2
3
4
5
...