Boltzmann Equation Solver Adapted to Emergent Chemical Non-equilibrium
  We present a novel method to solve the spatially homogeneous and isotropic
relativistic Boltzmann equation. We employ a basis set of orthogonal
polynomials dynamically adapted to allow for emergence of chemical
non-equilibrium. Two time dependent parameters characterize the set of
orthogonal polynomials, the effective temperature $T(t)$ and phase space
occupation factor $\Upsilon(t)$. In this first paper we address (effectively)
massless fermions and derive dynamical equations for $T(t)$ and $\Upsilon(t)$
such that the zeroth order term of the basis alone captures the particle number
density and energy density of each particle distribution. We validate our
method and illustrate the reduced computational cost and the ability to easily
represent final state chemical non-equilibrium by studying a model problem that
is motivated by the physics of the neutrino freeze-out processes in the early
Universe, where the essential physical characteristics include reheating from
another disappearing particle component ($e^\pm$-annihilation).
