# Response Theory for Equilibrium and Non-Equilibrium Statistical Mechanics: Causality and Generalized Kramers-Kronig Relations

@article{Lucarini2008ResponseTF, title={Response Theory for Equilibrium and Non-Equilibrium Statistical Mechanics: Causality and Generalized Kramers-Kronig Relations}, author={Valerio Lucarini}, journal={Journal of Statistical Physics}, year={2008}, volume={131}, pages={543-558} }

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific…

## 53 Citations

Evidence of Dispersion Relations for the Nonlinear Response of the Lorenz 63 System

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The rigid separation between forcing and response is broken, which is key in linear response theory, and the concept of causality is revisited, finding that not all observables are equally good as predictors when a given forcing is applied.

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We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We first show that using a general functional decomposition for space–time dependent forcings, we…

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The perturbation theory of operator semigroups is used to derive response formulas for a variety of combinations of acting forcings and reference background dynamics. We decompose the response…

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Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach

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We consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have…

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