Self Assembly and Entropy
How are small and large scale systems formed when the
universe favours entropy?
It seems that the probability of forming them are very low.
Your question is the result of a common misunderstanding of the
Second Law of Thermodynamics. This misunderstanding has several
origins. The first misunderstanding is that processes that result
in a decrease in entropy cannot occur. This is an incorrect statement
of the Second Law. Every time water freezes the entropy of the
transition of water to ice decreases. The same can be said of many
other processes. The Second Law states the following: "Some things
happen -- other things do not." It is a succinct statement of many
billions of empirical observations. It is an empirical observation
that processes that can occur are accompanied by an increase in the
total change in entropy. That means not only the entropy change of
some parts of the total system (the Universe if you want to be grandiose
about it) but in practice the "system" is usually some small sub-set of
the Universe. There are many alternative, but equivalent, statements of
this observation. One alternative statement is that Nature left to itself
does not create gradients. A simple example is that a bar of metal at a
constant temperature does not, left to itself, evolve into a condition
where one end of the bar is hotter / colder than the other. Another is
that a balloon, pricked by a pin, does not "unpop". It always "pops".
Because the Second Law is a statistical rule, there is a remote, a very
very remote possibility that it could "unpop", but the probability
(which can actually be computed) is older than the age of the Universe,
so betting on "unpoping" is not a very good bet.
Saying that the "Universe favors entropy" is misleading because the
niverse does not have a choice in the matter. A clearer, more correct
statement of the Second Law is this: "Some things (events) happen; some
things do not." Those events which happen are associated with an increase
in the TOTAL entropy change calculated according to a set of very specific
set of rules. That does not mean that there cannot be "local" decreases
in entropy, sometimes very large decreases. Every event that has ever
been observed to occur, always has associated with it a positive increase
in the TOTAL entropy. Repeating -- this does not mean that there cannot be
"local" decreases in entropy -- it means that the TOTAL entropy is positive.
Historically, "the Universe" got involved in statements of the Second Law,
which is unfortunate because in the translation from German to English the
term "Universe" takes on a philosophical context that in not intended in the
original language. There is nothing mysterious about the Second Law if you
keep in mind the empirical statement that, "Some things happen. Some things
do not." And also remember that the ultimate "happening" or "not happening"
has nothing to do with the speed of it happening. It only refers to the
ultimate "possibility" or ultimate "impossibility" of the event occurring.
Entropy is not just a matter of how matter is distributed in space. The
other factor to consider is the distribution of energy. Just as entropy is
maximized by the dispersion of matter, it is also maximized by the dispersion
of energy. In many processes, these two tendencies work in opposite directions.
A classic example of this interplay is the formation of a star by the
gravitational collapse of a cloud of gas. Clearly, such a process causes
matter to become more localized rather than more dispersed. How can this be
consistent with the fact that all processes that actually occur act to increase
entropy? The answer is the distribution of energy. The dispersed gas cloud has
fairly high potential energy, since all the molecules of gas, which attract each
other gravitationally, are far apart. As they move together under the force of
their mutual gravitational attraction, they speed up. So, as their potential
energy decreases, their kinetic energy increases by the same amount. In fact,
if that were all there was to the story, the gas cloud never could actually
collapse. The molecules would be moving so fast when they are close together
that they would never stay close: they would simply zoom back out just as
separated as they were at the beginning.
The key is that their kinetic energy is sapped by another process: radiation.
As the molecules move faster, they become hotter (temperature basically IS
molecular kinetic energy). Hot things emit more electromagnetic radiation than
cold things, and some of this radiation escapes the collapsing cloud entirely.
Thus, the cloud can continue to collapse, and the molecules come closer together,
even while getting hotter. Matter becomes more localized, but energy is
radiating out into space, beyond the dimensions of the original gas cloud.
When you take energy into account, you see that the entropy of the universe is
All other spontaneous processes that cause matter to become localized involve a
compensating delocalization of energy, typically as the production of heat or
Department of Physics and Astronomy
University of Wyoming
Click here to return to the Material Science Archives
Update: June 2012