We show that the van der Waals gas does not exhibit just the celebrated liquid-gas 1 transition but also a quantum-classical one. We study the issue with reference to the LMC statistical 2 complexity and in relation to the order-disorder contrast.

We investigate the physics of a medium-size quantum particle' gases, of the order of hundreds or thousands of fermions/bosons (far below the thermodynamic limit $N \, \rightarrow \, 10^{24}$). Appeal to microcanonical ensemble becomes then unavoidable. The so-called statistical complexity is our protagonist. Interesting facts are uncovered, both for fermions and bosons, yielded by statistical quantifiers.

In this paper we establish information theoretical bridges between 1) Thermal Heisenberg uncertainties $\Delta x \Delta p$ (at temperature $T$), and 2) LMC structural quantifiers. After having achieved such purpose, we determine to what an extent our bridges can be extended to both the semi classical and classical realms. Also, we find a strict bound relating a special LMC structural quantifier to quantum uncertainties.