ilya_prigogine_isabelle_stengers_alvin_tofflerbookfi-org

ORDER OUT OF CHAOS 142
organization. Part of the energy of the system, which in laminar
flow was in the thermal motion of the molecules, is being
transferred to macroscopic organized motion.
The "Benard instability" is another striking example of the
instability of a stationary state giving rise to a phenomenon of
spontaneous self-organization. The instability is due to a vertical
temperature gradient set up in a horizontal liquid layer. The
lower surface of the latter is heated to a given temperature,
which is higher than that of the upper surface. As a result of
these boundary conditions, a permanent heat flux is set up,
moving from the bottom to the top. When the imposed gradient
reaches a threshold value, the fluid's state of rest-the
stationary state in which heat is conveyed by conduction
alone, without convection-becomes unstable. A convection
corresponding to the coherent motion of ensembles of molecules
is produced, increasing the rate of heat transfer. Therefore,
for given values of the constraints (the gradient of
temperature), the entropy production of the system is increased;
this contrasts with the theorem of minimum entropy
production. The Benard instability is a spectacular phenomenon.
The convection motion produced actually consists
of the complex spatial organization of the system. Millions of
molecules move coherently, forming hexagonal convection
cells of a characteristic size.
In Chapter IV we introduced Boltzmann's order principle,
which relates entropy to probability as expressed by the number
of complexions P. Can we apply this relation here? To each
distribution of the velocities of the molecules corresponds a
number of complexions. This number measures the number of
ways in which we can realize the velocity distribution by attributing
some velocity to each molecule. The argument runs
parallel to that in Chapter IV, where we expressed the number
of complexions in terms of the distributions of molecules between
two boxes. Here also the number of complexions is
large when there is disorder-that is, a wide dispersion of velocities.
In contrast, coherent motion means that many molecules
travel with nearly the same speed (small dispersion of
velocities). To such a distribution corresponds a number of
complexions P so low that there seems almost no chance for
the phenomenon of self-organization to occur. Yet it occurs!
We see, therefore, that calculating the number of complexions,