  The second entropy theory for non-equilibrium thermodynamics is used to show
that the optimum structure or pattern of a time-dependent system corresponds to
the maximum entropy. A formula for the total entropy of convective heat flow is
derived. The Navier-Stokes equations in Boussinesq approximation for straight
roll convection are solved by a Fourier expansion technique. Results for the
velocity amplitude are in good agreement with previous computations and
experimental measurements. For the spontaneous transitions between straight
roll states reported in the literature, it is shown that the measured change in
convective pattern wave length corresponds to an increase in the entropy.
  This paper has been superseded by arXiv:1208.5105v1.
