  In recent years, much study has been made by applying the {\it non-extensive
statistics} (NES) to various non-extensive systems where the entropy and/or
energy are not necessarily proportional to the number of their constituent
subsystems. The non-extensivity may be realized in many systems such as
physical, chemical and biological ones, and also in small-scale nanosystems.
  After briefly reviewing the recent development in nanomagnetism and the NES,
I have discussed, in this article, NES calculations of thermodynamical
properties of a nanocluster containing noninteracting $M$ dimers. With bearing
in mind a transition-metal nanocluster, each of the dimers is assume to be
described by the two-site Hubbard model ({\it a Hubbard dimer}). The
temperature and magnetic-field dependences of the specific heat, magnetization
and susceptibility have been calculated by changing M=1, 2, 3 and $\infty$,
results for $M=\infty$ corresponding to those of the conventional
Boltzman-Gibbs statistics (BGS). It has been shown that the thermodynamical
property of nanoclusters containing a small number of dimers is considerably
different from that of macroscopic counterparts calculated within the BGS The
specific heat and susceptibility of spin dimers described by the Heisenberg
model have been discussed also by employing the NES.
