Neutron Star formation Entropy

When a neutron star forms, is its entropy lower than when it was in the form of the star core. In the case of a black hole the entropy becomes the surface area, so what happens in a neutron star because the neutron star doesn't get significantly brighter from the collapse and the matter in the neutron star is in a more ordered state than pure hydrogen or helium. So does that mean entropy drops in neutron star formations because entropy is not yet related to surface area because it is not a black hole just yet?

Entropy never spontaneously drops in macroscopic systems. This is the second law of thermodynamics. Local decreases in entropy, due to e.g. crystallization, are always offset by entropy increases elsewhere in the system.

I don't know whether we have an expression for the entropy per unit volume in the nuclear material that makes up a neutron star. But even if neutron star matter has relatively low entropy, lots of other particles are emitted when the neutron star forms. The entropy of the entire system includes the entropy of this emitted radiation.

In a comment, you suggest that you might be confusing the entropy of a system with the entropy of the particles that make up the system. In statistical mechanics, the entropy is

$$S = k\log\Omega$$

where $$k$$ is Boltzmann's unit-conversion constant, and $$\Omega$$ is the number of indistinguishable microscopic states that your system could occupy to give its other state variables, like temperature and pressure and whatever.

For instance, suppose you go the the party store and buy a cylinder of helium for balloons. Helium is a monoatomic gas, and at room temperature all of the atoms are in their electronic ground states. There isn't any degeneracy in the helium ground state, so each atom has $$\Omega=1$$: there is zero entropy in each atom, because there's only one way for a helium atom to occupy its ground state.

Now suppose you take that gas cylinder, put it in a vacuum chamber so we aren't distracted by other gases, and open the regulator. Immediately you have an entropy-increasing process. There are lots more ways for the helium to fill the space inside and outside the cylinder than there are for the helium to all stay inside the cylinder. So the helium escapes from the cylinder into its environment. The gas will never spontaneously all return to the cylinder, because that would decrease the entropy of the entire system.

The entropy in the photons and neutrinos and fission fragments that escape from a neutron star as it forms isn't stored in the particles. The entropy is stored in the momentum distribution of the particles. I don't know whether dense neutron matter is a high- or low-entropy medium. But when a neutron star forms, the entropy of the neutron core plus the entropy of the emitted radiation and detritus is larger than the entropy of the initial star.

• Only neutrinos and photons are emitted for the most part and those have low entropy right? Commented Feb 29 at 2:01