Multifield Stochastic Particle Production: Beyond a Maximum Entropy
  Ansatz
  We explore non-adiabatic particle production for $N_{\rm f}$ coupled scalar
fields in a time-dependent background with stochastically varying effective
masses, cross-couplings and intervals between interactions. Under the
assumption of weak scattering per interaction, we provide a framework for
calculating the typical particle production rates after a large number of
interactions. After setting up the framework, for analytic tractability, we
consider interactions (effective masses and cross couplings) characterized by
series of Dirac-delta functions in time with amplitudes and locations drawn
from different distributions. Without assuming that the fields are
statistically equivalent, we present closed form results (up to quadratures)
for the asymptotic particle production rates for the $N_{\rm f}=1$ and $N_{\rm
f}=2$ cases. We also present results for the general $N_{\rm f} >2$ case, but
with more restrictive assumptions. We find agreement between our analytic
results and direct numerical calculations of the total occupation number of the
produced particles, with departures that can be explained in terms of violation
of our assumptions.
  We elucidate the precise connection between the maximum entropy ansatz (MEA)
used in Amin & Baumann (2015) and the underlying statistical distribution of
the self and cross couplings. We provide and justify a simple to use
(MEA-inspired) expression for the particle production rate, which agrees with
our more detailed treatment when the parameters characterizing the effective
mass and cross-couplings between fields are all comparable to each other.
However, deviations are seen when some parameters differ significantly from
others. We show that such deviations become negligible for a broad range of
parameters when $N_{\rm f}\gg 1$.
