This could be at least a partial answer.
Degenerate stars can only exist up to a maximal mass, the Chandrasekhar mass.
There needs to be an equilibrium between the gravitational pull and outward pressure.
For very dense stars, like white dwarfs, gas pressure and it's kinetic energy doesn't play a significant role anymore.
Instead it needs to come from the density itself. For an electron gas (or Fermi gas) the pressure comes from the exclusion principle of Pauli, stating that no two electrons can occupy the same state.
The less space that is available for the electrons the higher the mean impulse (Heisenberg's uncertainty relation). This results in mean kinetic energy that is inverse dependant on mass.
Electrons are lighter and have higher (Fermi) energy. The pressure due to protons can be neglected.
For neutron stars he pressure has to come from neutrons obviously.
This has been described in great detail in:
- Roman Sexl Hannelore Sexl WHITE DWARFS-BLACK Holes An introduction to Relativistic Astrophysics
I don't know if there is a more modern or more suitable book or reference.