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

TL;DR

This paper demonstrates that non-ergodic renewal processes can maintain a persistent response to stimuli, challenging the notion of the 'death of linear response' and highlighting the significance of 1/f-noise in complex systems.

Contribution

It introduces a method to sustain a linear response in non-ergodic renewal processes by using similar non-ergodic stimuli, extending understanding of information transport.

Findings

Persistent correlation between stimulus and response in non-ergodic processes.

1/f-noise corresponds to a singularity with experimental relevance.

Linear response can be maintained beyond traditional limits.

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.