  We have determined the entropy, the total energy, and the specific heat of
the systems consisting of $M\geq 3$ hydrogen molecules. The calculations were
conducted in the framework of the nonextensive Tsallis statistics. The relation
between $M$ and the entropic index $q$ is given by $q = 1 + 1/M$, which results
from the fact that the temperature of the nanosystems fluctuates around the
temperature of the reservoir (Wilk and W{\l}odarczyk, Phys. Rev. Lett. {\bf
84}, 2770 (2000)). The electron energy states of the hydrogen molecule have
been determined with the help of the Hubbard Hamiltonian, which models all
two-body interactions. The Hubbard Hamiltonian integrals have been calculated
by using the variational method, whereas the Wannier function has been
associated with $1s$ Slater-type orbitals. We have included the contributions
to the energy of the hydrogen molecule coming from the oscillatory (either
harmonic or anharmonic), rotational and translational degrees of freedom. In
addition, we have investigated the impact of the external force ($F$) or the
magnetic field ($h$) on the thermodynamic parameters of the systems. In each
case the noticeable deviation from the results of the classical statistical
physics can be observed for the systems consisting of $M<M_{c}\sim 10^{3}$
molecules.
