  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.
