Speaker
Description
Biological systems need to react to stimuli over a broad spectrum of timescales. If and how this
ability can emerge without external fine-tuning is a puzzle. This problem has been considered in
discrete Markovian systems where results from random matrix theory could be leveraged. Indeed,
generic large transition matrices are governed by universal results, which predict the absence of
long timescales unless fine-tuned. Previous work has considered an ensemble of transition matrices
and motivated a temperature-like variable that controls the dynamic range of matrix elements.
Findings were applied to fMRI data from 820 human subjects scanned at wakeful rest. The data
was quantitatively understood in terms of the random model, and brain activity was shown to
lie close to a phase transition when engaged in unconstrained, task-free cognition – supporting
the brain criticality hypothesis in this context. In this work, the model is advanced in order to
discuss the effect of matrix asymmetry, which controls entropy production, on the previous results.
We introduce a new parameter that controls the asymmetry of these discrete Markovian systems
and show that when varied over an appropriate scale this factor is able to collapse Shannon entropy
measures. This collapse indicates that structure emerges over a dynamic range of both temperatures
and asymmetry, and allows a phase diagram of temperature in discrete Markovian systems
to be produced.
