Non-Equilibrium Pattern Formation vs Equilibrium Phase Transitions

The Benard cell example illustrates some features of non-equlibrium pattern formation (thus order creation) that are similar to those of second-order phase transitions in equilibrium systems. Let us list these [1]:

1. In both cases the pattern formation depends on a parameter crossing some value (e.g. compare the Ising model with the Benard cell example).
2. There is a change of symmetry as the threshold is crossed.
3. Dissipative structures show order at a length scale that is much larger than the intrinsic microscopic length scale. That is, a large correlation length emerges that allows the system to organise itself at a collective level. This is similar to what happens near a second order phase transition.

However there are also some differences:

1. In non-equilibrium systems it is impossible in general to determine the exact pattern that will be formed (that is the exact way that the symmetry will be broken) as the system is usually sensitive to various details and noise. By contrast the state of an equilibrium system is uniquely determined by various extremal principles like the minimization of free energy. (Thus there is more variety in the patterns that can form in non-equilibrium cases, as Nature proves !)
2. The final (away from the transition point) order or pattern in equilibrium systems shows a characteristic length scale similar to that of the underlying level. However the patterns in non-equilibrium systems have no relation to the underlying structure. In fact the large correlation length of dissipative structures is a classic example of an emergent property!