# QCD: In some phase diagrams, the axis are temperature and baryon chemical potential - what does it have to do with densities?

In this figure

one axis is the temperature (this one is no problem), the other one is the baryon chemical potential which causes my confusion.
Figure from here: Phase diagram of simplified QCD.
The text I'm referring to (with a similar figure): http://www.fair-center.eu/for-users/experiments/cbm/introduction.html.

Anyway, in a text about phases of QCD, the authors referred to this x-axis as the density and not the baryon chemical potential.
So my questions are:
What is the baryon chemical potential? What does it tell me?
What does it have to do with densities? Is it just a "synonym" for densities?
Also, as far as I understood, the phases aren't like the phases of "normal" matter, e.g. hadronic matter is at 0 K and 300 million tons per cm3 (see the link for the text) in a "liquid" phase. So, what do the phases look like? Why is it "liquid" and not liquid?

As far as its relation to density, the best answer I could find is for the case of a Fermi gas: http://www.physics.udel.edu/~glyde/PHYS825/Lectures/chapter_8.pdf. Here, it is shown that the Fermi momentum $p_F$ is dependent on density$^{1/3}$. Since the Fermi energy is proportional to $p_F^2$, it is also proportional to density$^{2/3}$. The chemical potential is proportional to the Fermi energy, so it is also proportional to density$^{2/3}$.