Relevance of sampling schemes in light of Ruelle's linear response theory
Abstract
We reconsider the theory of the linear response of nonequilibrium steady states to perturbations. We first show that using a general functional decomposition for spacetime dependent forcings, we can define elementary susceptibilities that allow us to construct the linear response of the system to general perturbations. Starting from the definition of SRB measure, we then study the consequence of taking different sampling schemes for analysing the response of the system. We show that only a specific choice of the time horizon for evaluating the response of the system to a general timedependent perturbation allows us to obtain the formula first presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be finetuned to make the definition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analysing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick.
 Publication:

Nonlinearity
 Pub Date:
 May 2012
 DOI:
 10.1088/09517715/25/5/1311
 arXiv:
 arXiv:1105.2527
 Bibcode:
 2012Nonli..25.1311L
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 Nonlinear Sciences  Chaotic Dynamics;
 Physics  Computational Physics
 EPrint:
 21 pages, 1 figures