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

Beyond the linear fluctuation-dissipation theorem: the role of causality In this paper we tackle the traditional problem of relating the fluctuations of a system toits response to external forcings and extend the classical theory in order to beable to encompass also nonlinear processes. With this goal, we try to build onKubos linear response theory and the response theory recently developed byRuelle for nonequilibrium systems equipped with an invariant SinaiRuelleBowen(SRB) measure. Our derivation also sheds light on the link between causalityand the possibility of relating fluctuations and response, both at the linear andnonlinear level. We first show, in a rather general setting, how the formalism ofRuelles response theory can be used to derive in a novel way a generalizationof the KramersKronig relations. We then provide a formal extension at eachorder of nonlinearity of the fluctuation-dissipation theorem for general systemsendowed with a smooth invariant measure. Finally, we focus on the physicallyrelevant case of systems weakly perturbed from equilibrium, for which we presentexplicit fluctuation-dissipation relations linking the susceptibility describing thenth order response of the system with suitably defined correlations taken in the equilibriumensemble. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Statistical Mechanics: Theory and Experiment IOP Publishing

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

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Copyright
Copyright IOP Publishing Ltd
eISSN
1742-5468
DOI
10.1088/1742-5468/2012/05/P05013
Publisher site
See Article on Publisher Site

Abstract

In this paper we tackle the traditional problem of relating the fluctuations of a system toits response to external forcings and extend the classical theory in order to beable to encompass also nonlinear processes. With this goal, we try to build onKubos linear response theory and the response theory recently developed byRuelle for nonequilibrium systems equipped with an invariant SinaiRuelleBowen(SRB) measure. Our derivation also sheds light on the link between causalityand the possibility of relating fluctuations and response, both at the linear andnonlinear level. We first show, in a rather general setting, how the formalism ofRuelles response theory can be used to derive in a novel way a generalizationof the KramersKronig relations. We then provide a formal extension at eachorder of nonlinearity of the fluctuation-dissipation theorem for general systemsendowed with a smooth invariant measure. Finally, we focus on the physicallyrelevant case of systems weakly perturbed from equilibrium, for which we presentexplicit fluctuation-dissipation relations linking the susceptibility describing thenth order response of the system with suitably defined correlations taken in the equilibriumensemble.

Journal

Journal of Statistical Mechanics: Theory and ExperimentIOP Publishing

Published: May 1, 2012

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