  The cortex exhibits self-sustained highly-irregular activity even under
resting conditions, whose origin and function need to be fully understood. It
is believed that this can be described as an "asynchronous state" stemming from
the balance between excitation and inhibition, with important consequences for
information-processing, though a competing hypothesis claims it stems from
critical dynamics. By analyzing a parsimonious neural-network model with
excitatory and inhibitory interactions, we elucidate a noise-induced mechanism
called "Jensen's force" responsible for the emergence of a novel phase of
arbitrarily-low but self-sustained activity, which reproduces all the
experimental features of asynchronous states. The simplicity of our framework
allows for a deep understanding of asynchronous states from a broad
statistical-mechanics perspective and of the phase transitions to other
standard phases it exhibits, opening the door to reconcile, asynchronous-state
and critical-state hypotheses. We argue that Jensen's forces are measurable
experimentally and might be relevant in contexts beyond neuroscience.
