interactions are solved for together in a quantum-kinetic approach [@vlasenko:14a].

-   **Equation of State and Nuclear Reactions.** The EOS is essential for the (M)HD part of the problem and for updating the matter thermodynamics after neutrino-matter interactions. Baryons (proton, neutrons, alpha particles, heavy nuclei), electrons, positrons, and photons contribute to the EOS. Neutrino momentum transfer contributes an effective pressure that is taken into account separately since neutrinos are not everywhere in local thermodynamic equilibrium with the stellar plasma. In different parts of the star, different EOS physics applies.

    At low densities and temperatures below $\sim$$0.5\,\mathrm{MeV}$ ($\sim$$5\times 10^9\,\mathrm{K}$), nuclear reactions are too slow to reach nuclear statistical equilibrium. In this regime, the mass fractions of the various heavy nuclei (isotopes, in the following) must be tracked explicitly. As the core collapses, the gas heats up and nuclear burning must be tracked with a nuclear reaction network, a stiff system of ODEs. Solving the reaction network requires the inversion of sparse matrices at each grid point. Depending on the number of isotopes tracked (ranging, typically from $\mathcal{O}(10)$ to $\mathcal{O}(100)$), nuclear burning can be a significant contributor to the overall computational cost of a simulation. The EOS in the burning regime is simple, 