  The thermodynamic limit of the internal energy and the entropy of the system
of quantum interacting particles in random medium is shown to exist under the
crucial requirements of stability and temperedness of interactions. The energy
turns out to be proportional to the number of particles and/or volume of the
system in the thermodynamic limit. The obtained results require very general
assumptions on the random one-particle model. The methods are mainly based on
subadditive type inequalities.
