Once Before Time - Martin Bojowald [119]
ENTROPY:
DISORDERLY CONDUCT
Can’t bring back time. Like holding water in your hand. Would you go back to then? Just beginning then. Would you?
—JAMES JOYCE, Ulysses
Most processes of life do not involve just a few clearly defined bodies such as the planets, but rely on the motion of innumerable atoms, impossible to follow individually. To organize such a mess, measurements as well as theoretical descriptions focus on collective quantities of all microscopic constituents, such as the combined volume they occupy, their pressure (as a measure of the total force acting via atomic impacts on a surrounding wall), or their temperature (as a measure of the average velocity of all particles).
Many of these collective quantities, in contrast to the host of all the atomic positions, generally change in a manner not reversible in time. This is well known from daily life, for the shape of a mug, as a collective quantity for all its constituents, changes dramatically when it breaks, without easily reattaining its original form. The temporal process of a jar breaking into pieces is clearly distinguishable from the pieces flying in miraculous formation, merging into an undamaged jar. One can easily distinguish a movie of the breaking from its temporal reversal, something impossible to do for the molecular motion.
The contradiction between the temporal reversibility of the motion of the microscopic constituents of a mug on one hand, and the macroscopic irreversibility of the whole mug’s motion on the other, finds its explanation in the special form of the initial conditions required for a specific collective quantity such as the shape. Falling down toward the ground where it will break, the mug’s constituents have highly coordinated initial positions and velocities. The broken mug, by contrast, is splintered into many single parts whose positions, orientations, and velocities are all very different from one another. Only with much difficulty could one set them in motion so as to recombine into a whole vessel in a temporal reversion of the breaking.
One major difference between an intact and a broken mug is the state of order. In an unbroken mug, all constituents as well as their velocities are, by their very construction, precisely arranged and related to one another. In a broken mug, the order is partially eliminated along with cohesion; splinters can lie arbitrarily in space. An intact mug is in a much more special state than a broken one, there being many more configurations to be recognized in a broken vessel than in an intact one. The physical measure of this kind of disorder is called entropy, defined by the number of microscopic states corresponding to the numberless atomic positions in a macroscopic state specified by a few collective quantities. Entropy is low for an intact vessel, but high for a broken one; and it normally grows larger much more easily than smaller. The jar was created in a state of low entropy, only to break at a later time, or at least become worn and inevitably reach a state of higher entropy.
But how can one manage to construct a jar of low entropy in the first place? The material must be formed in a special way, and stabilized in a process that lowers the entropy. This is possible only by using energy, gained for instance by burning fuel such as coal or oil. Burning itself is a process whereby entropy is increased, as an ordered solid or liquid substance whose constituents must to a certain degree move in a coordinated way is transformed into an unordered gas of higher entropy. The entropy of the fuel must be increased in order to fabricate a vessel of lower entropy. As one can show on general grounds, entropy production through burning always exceeds the loss of entropy from producing an ordered piece. Viewing all ingredients, entropy indeed cannot decrease.
In this way, an imbalance between