b. How can one raise the chemical potential of a quasi particle gas?
For recapitulation (see section 1e): The chemical potential is the slope of the free energy of a gas with respect to the particle number in its present state.
In an atom gas the chemical potential has some fixed value, depending on the number of atoms in the gas and other parameters like pressure and temperature.
On the contrary, the number of particles in a gas of quasi-particles is not fixed! So the gas can choose with what number of particles it is most comfortable. And we know that every physical system tries to minimize its free energy. So the system will choose the particle number in such a way, that the free energy is minimized. This means that every quasi-particle system will, sooner or later, reach a point where its free energy is minimized with respect to the particle number. And we know that the slope of a function in its minimum is always zero. Therefore every quasi-particle gas will sooner or later reach a state where its chemical potential becomes zero. The gas will stay in this state until it is perturbed. This state is then called thermal equilibrium.
We see that there is no way to raise the chemical potential of a quasi-particle gas in total thermal equilibrium. So we have to think about a quasi-particle gas out of total thermal equilibrium.
For this we have to look deep inside the mechanisms that create and destroy these particles.
Such an analysis can only be carried out for a specific quasi-particle system, as different quasi particles are created and destroyed through different mechanisms.
From now on I will restrict myself to the description of a magnon gas in a thin (~5µm) ferromagnetic and electrically isolating crystal, that is placed in a magnetic field. In our case Yttrium Iron Garnet (YIG) with the chemical composition Y3Fe2(FeO3)3
The next section will treat the question:
What are the creation and destruction mechanisms for magnons?