Advanced burning and nuclear statistical equilibrium

Define $Y_i=n_i/n_b$ as the number of nuclei of species $i$ per baryon, where $n_b$ is total baryon density. The mass-number-weighted sum is one, and the charge-weighted sum gives the net electron fraction in neutral matter. This dimensionless convention differs from a molar abundance and must be stated before interpreting a network table. Nuclear mass fractions are approximately mass number times abundance when binding-energy corrections to the mass normalization are neglected.

For strong and electromagnetic reactions in full equilibrium, a nucleus containing a specified number of protons and neutrons has a chemical potential equal to the corresponding sum of nucleon chemical potentials. Rest masses must be included consistently. Nuclear masses, excited-state partition functions, density, and temperature then enter the equilibrium populations. A nucleus with high binding energy can be favored, but entropy and the charge constraint can keep substantial populations in alpha particles, free nucleons, or several heavy species rather than placing everything in one favored nucleus.

Strong and electromagnetic reactions conserve the total proton charge carried by baryons, so they cannot independently select the electron fraction. Electron captures and beta decays can change it, often on a different timescale. An NSE calculation at fixed electron fraction is therefore compatible with continuing slow weak evolution. Recomputing the equilibrium strong composition as the weak sector changes is a useful approximation when the timescale hierarchy remains valid, but fixing the electron fraction permanently would discard that evolution.

Beta equilibrium is an additional condition. For thermal trapped neutrinos, the chemical-potential balance of neutron plus electron-neutrino conversion into proton plus electron includes the neutrino chemical potential. In neutrino-transparent matter, escaping neutrinos are not automatically a thermal bath, so kinetic weak-rate balance must be checked rather than blindly imposing the same trapped-matter formula with a zero substituted. Neutrino transport, electron degeneracy, and actual capture and decay rates determine whether any weak stationary state can be approached on the available time.

Compare the slowest relevant equilibration mode of the strong network with the environmental timescale. If it is fast, strong composition can track equilibrium as temperature and density change. If only subsets equilibrate, quasi-statistical equilibrium groups can remain internally balanced while their intergroup abundances evolve kinetically. A high temperature by itself is not sufficient: density affects capture rates, bottlenecks can be slow, and a rapidly expanding parcel can leave insufficient time to establish the proposed equilibrium.

Cooling eventually breaks the balance of forward and reverse reactions. The final abundance pattern then depends on freezeout, residual captures, alpha availability, and weak evolution, not just on the equilibrium composition at the highest temperature. An iron-group-rich state is a useful physical possibility, but a universal claim that advanced burning always leaves pure iron would ignore electron fraction and trajectory. The worked mixture below checks conservation only; it does not pretend that those two species alone solve the thermodynamic minimization for any real stellar conditions.