2011/05/31 by Gerardo Aquino, Mauro Bologna, Paolo Grigolini +1 · 68 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Algorithm #Artificial intelligence #Computer science #Discrete mathematics #Dissipation #Ideal (ethics) #Law #Limit (mathematics) #Mathematical analysis #Mathematics #Noise (video) #Nonlinear Dynamics and Pattern Formation #Physics #Telecommunications #Thermodynamics #Transmission (telecommunications) #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.83.051130
published in Physical Review E 83(5), 051130 (American Physical Society) · 14 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1007.2917
openalex publication_date 2011/05/31 · arxiv created 2011/12/23 · arxiv updated 2015/06/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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/f^3\ensuremath-\ensuremathμ, the case \ensuremathμ=2 corresponding to ideal 1/f noise. We denote by \ensuremathμS and \ensuremathμP 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 \ensuremathμS<2 we have to set the condition \ensuremathμP<2. In the latter case, if \ensuremathμP<\ensuremathμS, the system S inherits the relaxation properties of the perturbing system. In the case where \ensuremathμP>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.