We analyze the phase-space compression, characteristic of all deterministic, dissipative systems for an inhomogeneous boundary-driven shear fluid via nonequilibrium molecular dynamics simulations. We find that, although the full system undergoes a phase space contraction, the marginal distribution of the fluid particles is described by a smooth, volume preserving probability density function. This is the case for most thermodynamic states of physical interest. Hence, we show that the models currently employed to investigate inhomogeneous fluids in a nonequilibrium steady state, in which only walls are thermostatted, generate a non-singular distribution for the fluid.
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