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We study a gas of hard rods on a ring, driven by an external thermostat, witheither elastic or inelastic collisions, which exhibits sub-diffusive behavior$<x^2 > \sim t^{1/2}$. We show the validity of the usualFluctuation-Dissipation (FD) relation, i.e. the proportionality between theresponse function and the correlation function, when the gas is elastic ordiluted. On the contrary, in strongly inelastic or dense cases, when the tracervelocity is no more independent of the other degrees of freedom, the Einsteinformula fails and must be replaced by a more general FD relation.

Fluctuation-Dissipation relation in sub-diffusive systems: the case of granular single-file