D Villamaina et al J. Stat. Mech. (2009) P07024 doi:10.1088/1742-5468/2009/07/P07024
D Villamaina1, A Baldassarri1,2, A Puglisi2 and A Vulpiani2,3
Show affiliationsWe discuss the well known Einstein and the Kubo fluctuation-dissipation relations (FDRs) in the wider framework of a generalized FDR for systems with a stationary probability distribution. A multivariate linear Langevin model, which includes dynamics with memory, is used as a treatable example to show how the usual relations are recovered only in particular cases. This study brings to the fore the ambiguities of a check of the FDR done without knowing the significant degrees of freedom and their coupling. An analogous scenario emerges in the dynamics of diluted shaken granular media. There, the correlation between position and velocity of particles, due to spatial inhomogeneities, induces violation of usual FDRs. The search for the appropriate correlation function which could restore the FDR can be more insightful than a definition of 'non-equilibrium' or 'effective temperatures'.
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) (See also 60H10)
Issue 07 (July 2009)
Received 6 April 2009, accepted for publication 3 June 2009
Published 14 July 2009
D Villamaina et al J. Stat. Mech. (2009) P07024
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