  In this paper we present a study of a general system coupled to a reservoir
consisting of nonlinear oscillators, based on perturbation theory at the
classical level. We extend the standard Zwanzig approach of elimination of bath
degrees of freedom order by order in perturbation. We observe that the
Fluctuation Dissipation Relation (FDR) in its standard form for harmonic baths
gets modified due to the nonlinearity and this is manifested through higher
powers of kBT in the expression for two-time noise correlation.As an aside, we
also observe that the first moment of the noise arising from a nonlinear bath
can be non-zero, even in absence of any external drive, if the reservoir
potential is asymmetric with respect to one of its minima, about which one
builds up the perturbation theory.
