ilya_prigogine_isabelle_stengers_alvin_tofflerbookfi-org

ORDER OUT OF CHAOS 178
Once again, only a statistical description is possible. The existence
of an instability may be viewed as the result of a fluctuation
that is first localized in a small part of the system and then
spreads and leads to a new macroscopic state.
This situation alters the traditional view of the relation between
the microscopic level as described by molecules or
atoms and the macroscopic level described in ter ms of global
variables such as concentration. In many situations fluctuations
correspond only to small corrections. As an example, let
us take a gas composed of N molecules enclosed in a vessel of
volume V. Let us divide this volume into two equal parts.
What is the number of particles X in one of these two parts?
Here the variable X is a "random" variable, and we would
expect it to have a value in the neighborhood of N/2.
A basic theorem in probability theory, the law of large numbers,
provides an estimate of the "error" due to fluctuations.
In essence, it states that if we measure X we have to expect a
value of the order N/2±v'Nii. If N is large, the difference
introduced by fluctuations v'Nfi may also be large (if
N= 1Q24, VN= 1012); however, the relative error introduced
by fluctuations is of the order of (v'N!i)/(N/2) or llYN and
thus tends toward zero for a sufficiently large value of N. As
soon as the system becomes large enough, the law of large
numbers enables us to make a clear distinction between mean
values and fluctuations, and the latter may be neglected.
Hewever, in nonequilibrium processes we may find just the
opposite situation. Fluctuations determine the global outcome.
We could say that instead of being corrections in the
average values, fluctuations now modify those averages. This
is a new situation. For this reason we would like to introduce a
neologism and call situations resulting from fluctuation "order
through fluctuation." Before giving examples, let us make
some general remarks to illustl·ate the conceptual novelty of
this situation.
Readers may be familiar with the Heisenberg uncertainty
relations, which express in a striking way the probabilistic aspects
of quantum theory. Since we can no longer simultaneously
measure position and coordinates in quantum theory,
classical determinism is breaking down. This was believed to
be of no importance for the description of macroscopic objects