Beyond the Death of Linear Response: 1/f optimal information transport

Abstract

Non-ergodic renewal processes have recently been shown by several authors to be insensitive to periodic perturbations, thereby apparently sanctioning the death of linear response, a building block of nonequilibrium statistical physics. We show that it is possible to go beyond the ``death of linear response" and establish a permanent correlation between an external stimulus and the response of a complex network generating non-ergodic renewal processes, by taking as stimulus a similar non-ergodic process. The ideal condition of 1/f-noise corresponds to a singularity that is expected to be relevant in several experimental conditions.

4 pages, 2 figures, 1 table, in press on Phys. Rev. Lett

References in corpus (7)

• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Distribution of Time-Averaged Observables for Weak Ergodicity Breaking
• The Physics of Living Neural Networks
• Use and Abuse of a Fractional Fokker-Planck Dynamics for Time-Dependent Driving
• Nonergodisity of a time series obeying Lévy statistics
• Ergodicity Breaking in a Deterministic Dynamical System
• Linear Response and Fluctuation Dissipation Theorem for non-Poissonian Renewal Processes

Cited by in corpus (12)

• Transmission of Information between Complex Networks: 1/f-Resonance
• Aging Wiener-Khinchin Theorem
• Analysis of cross-correlations in electroencephalogram signals as an approach to proactive diagnosis of schizophrenia
• Aging Wiener-Khinchin Theorem and Critical Exponents of $1/f$ Noise
• Complexity Measures of Music
• Quantum response theory for open systems and its application to Hall conductance
• Residence time statistics for $N$ blinking quantum dots and other stochastic processes
• Non-Ergodic Complexity Management
• Linear response theory and transient fluctuation theorems for diffusion processes: a backward point of view
• Weakly driven anomalous diffusion in non-ergodic regime: an analytical solution
• Spectral properties of stochastic processes possessing finite propagation velocity
• Scaling theory for the $1/f$ noise