  The theoretical model proposed by Einstein to describe the phononic specific
heat of solids as a function of temperature consists the very first application
of the concept of energy quantization to describe the physical properties of a
real system. Its central assumption lies in the consideration of a total energy
distribution among N (in the thermodynamic limit $N \rightarrow \infty$)
non-interacting oscillators vibrating at the same frequency ($\omega$).
Nowadays, it is well-known that most materials behave differently at the
nanoscale, having thus some cases physical properties with potential
technological applications. Here, a version of the Einstein's model composed of
a finite number of particles/oscillators is proposed. The main findings
obtained in the frame of the present work are: (i) a qualitative description of
the specific heat in the limit of low-temperatures for systems with nano-metric
dimensions; (ii) the observation that the corresponding chemical potential
function for finite solids becomes null at finite temperatures as observed in
the Bose-Einstein condensation and; (iii) emergence of a first-order like phase
transition driven by varying $N$.
