Beyond the linear fluctuation-dissipation theorem: the role of causality

Lucarini, V. ORCID: https://orcid.org/0000-0001-9392-1471 and Colangeli, M. (2012) Beyond the linear fluctuation-dissipation theorem: the role of causality. Journal of Statistical Mechanics: Theory and Experiment, 2012 (05). P05013. ISSN 1742-5468

Abstract/Summary

In this paper we tackle the traditional problem of relating the fluctuations of a system to its response to external forcings and extend the classical theory in order to be able to encompass also nonlinear processes. With this goal, we try to build on Kubo's linear response theory and the response theory recently developed by Ruelle for nonequilibrium systems equipped with an invariant Sinai-Ruelle-Bowen (SRB) measure. Our derivation also sheds light on the link between causality and the possibility of relating fluctuations and response, both at the linear and nonlinear level. We first show, in a rather general setting, how the formalism of Ruelle's response theory can be used to derive in a novel way a generalization of the Kramers–Kronig relations. We then provide a formal extension at each order of nonlinearity of the fluctuation-dissipation theorem for general systems endowed with a smooth invariant measure. Finally, we focus on the physically relevant case of systems weakly perturbed from equilibrium, for which we present explicit fluctuation-dissipation relations linking the susceptibility describing the n th order response of the system with suitably defined correlations taken in the equilibrium ensemble.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/71520
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	IOP Science
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