 In these cases, the time rate of entropy production has been shown to be a non-monotonic function of time during the approach to steady state heat convection.This makes these cases different from the near-thermodynamic-equilibrium regime of very-slow-transfer with linearity.Accordingly, the local time rate of entropy production, defined according to the local thermodynamic equilibrium hypothesis, is not an adequate variable for prediction of the time course of far-from-thermodynamic equilibrium processes.