cause thermonuclear fusion, and a star is born. If the star is large enough,
an even more dramatic entropy decrease is in the offing, as the star will
eventually explode in a supernova, a process that creates the heavy ele-
ments from which planets, and living things, can eventually form.Another Look at Entropy
Statistical mechanics offers an alternative definition of entropy. Statisti-
cal mechanics arose from the problem of discovering and utilizing the
vast amount of information there is in any assemblage of molecules. Any
sizable assemblage of molecules, such as a glass of water, contains at least
1024 molecules, each occupying a specific location (requiring three coor-
dinates to specify) and moving in three different directions (also requir-
ing three coordinates to specify the north-south velocity, the east-west
velocity, and the up-down velocity). Even if we could acquire knowledge
(which we can’t) of all this information for every molecule in the glass of
water, what on Earth would we do with it? Talk about information over-
load! If each computer had a terabyte of storage (a trillion bytes; I wouldn’t
be surprised if they’re on the market soon, if they’re not already) and each
coordinate used a single byte, you would need a computer for every man,
woman, and child on Earth simply to store that information about a glass
of water.
We encounter the same problem in analyzing the attributes of large as-
semblages of anything, such as the income distribution of the population
of the United States. The IRS undoubtedly has reasonably accurate date
for, say, 100 million people, but if we had a book with the information for
all 100 million people in it, our eyes would undoubtedly glaze as we tried
to examine it. Boil it all down to a small chart, such as the percentage of
people mak ing less t han $25,0 0 0, t he percentage mak ing bet ween $25,0 0 0
and $50,000, the percentage making between $50,000 and $75,000, the
percentage making between $75,000 and $100,000, and the percentage
making more than $100,000, and we are much more able to appreciate it
and use it to make decisions. Statistical mechanics was born when it was
realized that similar principles applied to the positions and motions of
large assemblages of molecules.
Any macrostate of a system, such as a glass of water with ice cubes in it,
is an assemblage of microstates—the temperature, velocity, and location
of the individual molecules. The definition of entropy offered by statisti-
cal mechanics is a measure of the number of microstates associated with
each macrostate. A glass of water with ice cubes in it has fewer micro-
states comprising it than a glass of water at a uniform temperature,
The Raw Materials 191