  A characteristic feature of thermalized non-equilibrated matter is that, in
spite of energy relaxation--equilibration, a phase memory of the way the
many-body system was excited remains. As an example, we analyze data on a
strong forward peaking of thermal proton yield in the Bi($\gamma$,p)
photonuclear reaction. New analysis shows that the phase relaxation in
highly-excited heavy nuclei can be 8 orders of magnitude or even much longer
than the energy relaxation. We argue that thermalized non-equilibrated matter
resembles a high temperature superconducting state in quantum many-body
systems. We briefly present results on the time-dependent correlation function
of the many-particle density fluctuations for such a superconducting state. It
should be of interest to experimentally search for manifestations of
thermalized non-equilibrated matter in many-body mesoscopic systems and
nanostructures.
