Fluctuation-dissipation relations for a nonlocal plasma

A generalized version of the Callen-Welton fluctuation-dissipation formula that is nonlocal in space and time is derived. In a nonuniform plasma there appear significant differences between the fluctuations of the electrostatic field and those of the electron density, and the spatial inhomogeneities lead to an asymmetry with respect to the sign inversion of the frequency.