  Spontaneous transitions between non-equilibrium patterns are characterised by
hydrodynamic calculations of ideal straight roll steady state heat convection.
The calculations are tested quantitatively against existing experimental data.
It is shown that at a given Rayleigh number the final wave number depends upon
whether the initial state was the conducting state, or, in the case of the
cross roll transition, the wave number of the initial straight roll state. The
final wave number does not correspond to the maximum or to the minimum heat
flux (entropy production or dissipation), nor to the maximum sub-system
entropy. In all cases the entropy of the total system increases monotonically
during the spontaneous transition. It is concluded that there does not exist
any single time thermodynamic property or variational principle for
non-equilibrium systems. It is further concluded that the second entropy is the
two time variational principle that determines the optimum non-equilibrium
state or pattern.
