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Relevance of sampling schemes in light of Ruelle's linear response theory

By Valerio Lucarini, Tobias Kuna, Jeroen Wouters and Davide Faranda

Abstract

We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We �rst show that by using a general functional decomposition for space-time dependent forcings, we can de�ne elementary susceptibilities that allow to construct the response of the system to general perturbations. Starting from the de�nition of SRB measure, we then study the consequence of taking di�erent sampling schemes for analysing the response of the system. We show that only a speci�c choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows to obtain the formula �rst presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be �ne-tuned to make the de�nition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analyzing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick

Publisher: IOP Publishing
Year: 2012
DOI identifier: 10.1088/0951-7715/25/5/1311
OAI identifier: oai:centaur.reading.ac.uk:27146
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