# Response Formulae for $n$-point Correlations in Statistical Mechanical Systems and Application to a Problem of Coarse Graining

@article{Lucarini2017ResponseFF, title={Response Formulae for \$n\$-point Correlations in Statistical Mechanical Systems and Application to a Problem of Coarse Graining}, author={Valerio Lucarini and Jeroen Wouters}, journal={arXiv: Statistical Mechanics}, year={2017} }

Predicting the response of a system to perturbations is a key challenge in mathematical and natural sciences. Under suitable conditions on the nature of the system, of the perturbation, and of the observables of interest, response theories allow to construct operators describing the smooth change of the invariant measure of the system of interest as a function of the small parameter controlling the intensity of the perturbation. In particular, response theories can be developed both for…

## 17 Citations

Response and Sensitivity Using Markov Chains

- MathematicsJournal of Statistical Physics
- 2020

Dynamical systems are often subject to forcing or changes in their governing parameters and it is of interest to study how this affects their statistical properties. A prominent real-life example of…

Quadratic response of random and deterministic dynamical systems.

- MathematicsChaos
- 2020

A general framework in which one can obtain rigorous convergence and formulas for linear and quadratic higher-order terms associated with the response of the statistical properties of a dynamical system to suitable small perturbations is shown.

A Statistical Mechanical Approach for the Parametrization of the Coupling in a Fast-Slow System

- Computer Science
- 2018

This work derives an expression for the deterministic and the stochastic component of the parametrization and shows that the approach allows for dealing seamlessly with the case of the Lorenz 63 being a fast as well as a slow forcing compared to the characteristic time scales ofThe Lorenz 84 model.

Reduced-order models for coupled dynamical systems: Data-driven methods and the Koopman operator.

- MathematicsChaos
- 2021

These findings support the physical basis and robustness of the EMR methodology and illustrate the practical relevance of the perturbative expansion used for deriving the parameterizations.

Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

- Mathematics
- 2018

The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal…

Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

- Computer ScienceNonlinear Processes in Geophysics
- 2018

This work derives an expression for the deterministic and the stochastic component of the parametrization and shows that the approach allows for dealing seamlessly with the case of the Lorenz 63 being a fast as well as a slow forcing compared to the characteristic timescales of thelorenz 84 model.

Reduced-Order Models for Coupled Dynamical Systems: Koopman Operator and Data-driven Methods.

- Mathematics
- 2020

These findings support the physical basis and robustness of the EMR methodology and illustrate the practical relevance of the perturbative expansion used for deriving the parametrizations.

Statistical mechanical methods for parametrization in geophysical fluid dynamics

- Environmental Science
- 2018

Scale-adaptive approach constructed using statistical mechanical arguments and composed by deterministic, stochastic and non-markovian contributions is studied and it is shown that comparisons based on the Wasserstein distance might be of relevance in many applications despite the curse of dimensionality.

Crisis of the Chaotic Attractor of a Climate Model: A Transfer Operator Approach

- Physics
- 2015

The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are characterised by a single or a pair of characteristic…

A proof of concept for scale‐adaptive parametrizations: the case of the Lorenz '96 model

- Mathematics
- 2016

A proof of concept of a scale-adaptive parameterization constructed using statistical mechanical arguments for fast variables that translates into deterministic, stochastic and non-markovian contributions to the equations of motion of the variables of interest is presented.

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