Sollich, P. and Fielding, S.M. and Mayer, P.
(2002)
*Fluctuation-dissipation relations and effective temperatures in simple non-mean field systems.*
Journal of Physics: Condensed Matter, 14.
pp. 1683-1696.
ISSN 1361-648X

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## Abstract

We give a brief review of violations of the fluctuation-dissipation theorem (FDT) in out-of-equilibrium systems; in mean field scenarios the corresponding fluctuation-dissipation (FD) plots can, in the limit of long times, be used to define a effective temperature Teff that shares many properties of the true thermodynamic temperature T. We discuss carefully how correlation and response functions need to be represented to obtain meaningful limiting FD plots in non-mean field systems. A minimum requirement on the resulting effective temperatures is that they should be independent of the observable whose correlator and response are being considered; we show for two simple models with glassy dynamics (Bouchaud's trap model and the Glauber-Ising chain at zero temperature) that this is generically not the case. Consequences for the wider applicability of effective temperatures derived from FD relations are discussed; one intriguing possibility is that at least the limit of the FDT violation factor for well separated times may generically be observable-independent and so could yield a meaningful Teff.

Item Type: | Article |
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Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics MSC 2010, the AMS's Mathematics Subject Classification > 82 Statistical mechanics, structure of matter |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 17 Jul 2006 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/387 |

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