  We present here for the first time a unifying perspective for the lack of
equipartition in non-linear ordered systems and the low temperature phase-space
fragmentation in disordered systems. We demonstrate that they are just two
manifestation of the same underlying phenomenon: ergodicity breaking. Inspired
by recent experiments, suggesting that lasing in optically active disordered
media is related to an ergodicity-breaking transition, we studied numerically a
statistical mechanics model for the nonlinearly coupled light modes in a
disordered medium under external pumping. Their collective behavior appears to
be akin to the one displayed around the ergodicity-breaking transition in
glasses, as we show measuring the glass order parameter of the
replica-symmetry-breaking theory. Most remarkably, we also find that at the
same critical point a breakdown of energy equipartition among light modes
occurs, the typical signature of ergodicity breaking in non-linear systems as
the celebrated Fermi-Pasta-Ulam model. The crucial ingredient of our system
which allows us to find equipartition breakdown together with replica symmetry
breaking is that the amplitudes of light modes are locally unbounded, i.e.,
they are only subject to a global constraint. The physics of random lasers
appears thus as a unique test-bed to develop under a unifying perspective the
study of ergodicity breaking in statistical disordered systems and non-linear
ordered ones.
