Fluctuation-dissipation relations and effectivetemperatures in simple non-mean field systems

Abstract

We give a brief review of violations of thefluctuation-dissipation theorem (FDT) in out-of-equilibriumsystems; in mean field scenarios the correspondingfluctuation-dissipation (FD) plots can, in the limit of longtimes, be used to define a effective temperature Teff that shares many properties of the true thermodynamictemperature T. We discuss carefully how correlation andresponse functions need to be represented to obtain meaningfullimiting FD plots in non-mean field systems. A minimumrequirement on the resulting effective temperatures is that theyshould be independent of the observable whose correlator andresponse are being considered; we show for two simple modelswith glassy dynamics (Bouchaud's trap model and theGlauber-Ising chain at zero temperature) that this isgenerically not the case. Consequences for the widerapplicability of effective temperatures derived from FDrelations are discussed; one intriguing possibility is that atleast the limit of the FDT violation factor for well separatedtimes may generically be observable-independent and so couldyield a meaningful Teff.