  Strictly speaking the laws of the conventional Statistical Physics, based on
the Equipartition Postulate and Ergodicity Hypothesis, apply only in the
presence of a heat bath. Until recently this restriction was not important for
real physical systems: a weak coupling with the bath was believed to be
sufficient. However, the progress in both quantum gases and solid state
coherent quantum devices demonstrates that the coupling to the bath can be
reduced dramatically. To describe such systems properly one should revisit the
very foundations of the Statistical Mechanics. We examine this general problem
for the case of the Josephson junction chain and show that it displays a novel
high temperature non-ergodic phase with finite resistance. With further
increase of the temperature the system undergoes a transition to the fully
localized state characterized by infinite resistance and exponentially long
relaxation.
