  We present two main results. The first is a plausible validation argument for
the principle of a maximal rate of entropy production for Euler equation
turbulence. This principle can be seen as an extension of the second law of
thermodynamics. In our second main result, we examine competing models for
large eddy simulations of Euler equation (fully developed) turbulence. We
compare schemes with no subgrid modeling, implicit large eddy simulation (ILES)
with limited subgrid modeling and those using dynamic subgrid scale models. Our
analysis is based upon three fundamental physical principles: conservation of
energy, the maximum entropy production rate and the principle of universality
for multifractal clustering of intermittency. We draw the conclusion that the
absence of subgrid modeling, or its partial inclusion in ILES solution violates
the maximum entropy dissipation rate admissibility criteria. We identify
circumstances in which the resulting errors have a minor effect on specific
observable quantities and situations where the effect is major.
  Application to numerical modeling of the deflagration to detonation
transition in type Ia supernova is discussed.
