  In recent work, we have shown that fundamental quantities such as the total
entropy production, the thermodynamic variables conjugate to the thermodynamic
forces, and the Glansdorff-Prigogine's dissipative variable may be discretized
at the mesoscopic scale. The Canonical Commutation Rules (CCRs) valid at the
mesoscopic scale have been postulated and the measurement process consists of
determining the eigenvalues of the operators associated with the thermodynamic
quantities. The essence of that work was to analyze the consequences of these
postulates. This letter aims to understand the physical nature of the new
constant (beta) introduced in the CCRs. In particular, two questions are still
open. Is beta a new fundamental constant? Does the constant in the CCRs
correspond to the lowest limit? We shall tackle the problem starting from the
simplest assumption: the expression of beta can be derived from a simple model
(a heuristic model) for nano-gas and studied through the tools of classical
statistical physics. We will find that the theoretical value is very close to
the experimental one. We shall not go further in our interpretation; we shall
limit ourselves simply by noticing that according to our model, the constant
beta does not appear to be a new fundamental constant but corresponds to the
minimum value.
