  We will present elementary scaling arguments focussed on the thermodynamics
in the proximity of the quantum critical point in the cuprate superconductors.
Extending the analysis centered on the Gr\"uneisen parameter by Rosch, Si and
coworkers to the cuprates, we demonstrate that a combination of specific heat-
and chemical potential measurements can reveal the nature of the zero
temperature singularity. From the known specific heat data it follows that the
effective number of time dimensions has to equal the number of space
dimensions, while we find a total of six scaling laws governing the temperature
and density dependence of the chemical potential, revealing directly the
coupling constant scaling dimension.
