Finite thermostats in classical and quantum nonequilibrium

Models for studying systems in stationary states but out of equilibrium have often empirical nature and very often break the fundamental time reversal symmetry. Here, a formal interpretation will be discussed of the widespread idea that, in any event, the particular friction model choice should not matter physically. The proposal is, quite generally, that for the same physical system a time reversible model should be possible. Examples about the Navier-Stokes equations are given.