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

Lucarini, V. ORCID: https://orcid.org/0000-0001-9392-1471, Kuna, T., Wouters, J. ORCID: https://orcid.org/0000-0001-5418-7657 and Faranda, D. (2012) Relevance of sampling schemes in light of Ruelle's linear response theory. Nonlinearity, 25 (5). p. 1311. ISSN 0951-7715 doi: 10.1088/0951-7715/25/5/1311

Abstract/Summary

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.