  From a minimal set made of four scale factors defined at the liquid-gas
critical point of a pure fluid, and one adjustable parameter which accounts for
particle quantum effects, we demonstrate here a master singular behavior of the
correlation length for the one-component fluid subclass, using an asymptotic
scale dilatation of the physical fields. Such master behavior observed within
the preasymtotic domain is in conformity with the renormalized $\Phi\_{d =
3}^{4}$ Field Theory predictions at large correlation length scale of the
fluctuating order parameter, for the complete universality class of the
symmetrical uniaxial 3D-Ising-like systems. The following consequences are
discussed: (i) A comparison between the critical state of pure fluids and the
zero-temperature state leads to an intuitive analogy with the (Nerst) third law
of thermo- dynamics, which authorizes specific master form for hyperscaling
within the subclass of pure fluids; (ii) A master constant value of the
non-dimensional critical entropy can exist for all the pure fluids at the
short-ranged lengthscale of the molecular interaction. From this latter
hypothesis, we show that the needed four scale factors are the four preferred
directions ex- pressing complete thermodynamic (linear) continuity crossing the
liquid-gas critical point on the (pressure, volume, temperature) phase surface.
