The linking of physics particle system in mean fields or interacting as multispecies systems can be viewed as a probabilistic model as envisioned by L. Boltzmann and G. Maxwell of dissipative stochastic dynamics of one or more species marking the birth of thermodynamics by expectations of statistical flows. In the early Twentieth Century, the introduction of electron and ions systems and the raise of particle charge and neutral particle dynamics the Boltzmann ideas were extended by Dirac and Fermi to encompassed an accurate model to describe electro-magnetic forces and braking of symmetry, and so the Boltzmann-Dirac-Fermi model arose as an accurate statistical frame work of understanding the hot-electron dynamics in solid states modeled by Boltzmann-Dirac-Fermi in terms of the statistical frameworks of thermodynamics for nanoelectronics. At the same time the raise of astrophysical systems, in the absence of easily observable experimental data become W. Pauli proposed neutral particles that can dissipate relativistic electron dynamics, and labeled them neutrinos and anti-neutrinos as a possible dissipative mechanisms. I will present a natural link between the probabilistic framework from Chapman-Kolmogorov flows the evolution of N-particle systems from different species that under ergodic assumptions that are sufficient for near space homogeneous system at the particle level for model reduction emerge a kinetic systems for neutrino and antineutrino particles couples to equations of relativized matter equations for rest mass density, with temperature and electron fraction rates depending on space-time, all in a spherical coordinate framework. We’ll discuss conservation properties for the system, entropies, and the natural Galerkin-Petrov kinetic scheme as a very efficient tool for fast solvers for this reduced model.