Transmission of information between complex systems: 1/f resonance

We study the transport of information between two complex systems with similar properties. Both systems generate non-Poisson renewal fluctuations with a power-law spectrum 1/f3^-μ, the case μ=2 corresponding to ideal 1/f noise. We denote by μ_S and μ_P the power-law indexes of the system of interest S and the perturbing system P, respectively. By adopting a generalized fluctuation-dissipation theorem (FDT) we show that the ideal condition of 1/f noise for both systems corresponds to maximal information transport. We prove that to make the system S respond when μ_S<2 we have to set the condition μ_P<2. In the latter case, if μ_P<μ_S, the system S inherits the relaxation properties of the perturbing system. In the case where μ_P>2, no response and no information transmission occurs in the long-time limit. We consider two possible generalizations of the fluctuation dissipation theorem and show that both lead to maximal information transport in the condition of 1/f noise.