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We construct different equivalent non-equilibrium statistical
ensembles in a $N$-degrees of freedom model of atmospheric turbulence,
introduced by Lorenz in 1996. The vector field can be decomposed into
an energy-conserving, time-reversible part, plus a non-time reversible
part, including forcing and dissipation. We construct a modified
version of the model where viscosity varies with time, in such a way
that energy is conserved, and the resulting dynamics is fully
time-reversible. The purpose is to test conjectures on a theory of
ensembles in non equilibrium statistical mechanics and turbulence as
well as the chaotic hypothesis and the fluctuation relation. This
leads to the proposal that using a model of a fluid where viscosity is
kept constant is just one option, and not necessarily the only option,
for describing accurately its statistical and dynamical properties.
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