# Quasi-Critical Brain Dynamics on a Non-Equilibrium Widom Line

arXiv: https://arxiv.org/abs/1405.6232 · HTML: https://mlsanity.com/paper/1405.6232/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2014.

## Built on by (most cited first, 2 of 2)

- [Toward a Physics of Deep Learning and Brains](https://mlsanity.com/paper/2509.22649/) (2025)
- [Turing's cascade instability supports the coordination of the mind, brain, and behavior](https://mlsanity.com/paper/2204.07904/) (2022)

## Abstract (arXiv)

Is the brain really operating at a critical point? We study the non-equilibrium properties of a neural network which models the dynamics of the neocortex and argue for optimal quasi-critical dynamics on the Widom line where the correlation length is maximal. We simulate the network and introduce an analytical mean-field approximation, characterize the non-equilibrium phase transition, and present a non-equilibrium phase diagram, which shows that in addition to an ordered and disordered phase, the system exhibits a quasiperiodic phase corresponding to synchronous activity in simulations which may be related to the pathological synchronization associated with epilepsy.