Emergence of biological complexity: Criticality, renewal and memory

The key purpose of this article is to establish a connection between two emerging fields of research in theoretical biology. The former focuses on the concept of criticality borrowed from physics that is expected to be extensible to biology through a robust theoretical approach that although not yet available shall eventually shed light into the origin of cognition. The latter, largely based on the tracking of single molecules diffusing in biological cells, is bringing to the general attention the need to go beyond the ergodic assumption currently done in the traditional statistical physics. We show that replacing critical slowing down with temporal complexity explains why biological systems at criticality are resilient and why long-range correlations are compatible with the free-will condition necessary for the emergence of cognition. Temporal complexity generates ergodicity breakdown and requires new forms of response of complex systems to external stimuli. We concisely illustrate these new forms of information transport and we also address the challenging issue of combining temporal complexity with coherence and renewal with infinite memory.