Dual Fluctuation–Dissipation Relationships between Tri- and Bispectra of the Brownian Motion

A fluctuation–dissipation analysis of nonlinear noise accompanying Brownian motion (BM) in electric systems is carried out. It is shown that, for symmetrical BM, there exists a linear set of dual fluctuation–dissipation relationships linking an equilibrium trispectrum to a derivative of a bispectrum with respect to a direct electric current (or voltage), taken at equilibrium. Analysis of an electrochemical model of BM in the form of a symmetrical slow discharge yields a proportionality coefficient.