Beyond the Death of Linear Response: 1/f- noise Resonance

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. We propose a theory for the transport of information through non-ergodic systems that explains why 1/f-noise is an efficient stimulus for complex systems. The ideal condition of 1/f-noise corresponds in fact to a singularity that is expected to be relevant in several experimental conditions of physical and biological interest.