The Information - James Gleick [130]
Order is subjective—in the eye of the beholder. Order and confusion are not the sorts of things a mathematician would try to define or measure. Or are they? If disorder corresponded to entropy, maybe it was ready for scientific treatment after all.
As an ideal case, the pioneers of thermodynamics considered a box of gas. Being made of atoms, it is far from simple or calm. It is a vast ensemble of agitating particles. Atoms were unseen and hypothetical, but these theorists—Clausius, Kelvin, Maxwell, Ludwig Boltzmann, Willard Gibbs—accepted the atomic nature of a fluid and tried to work out the consequences: mixing, violence, continuous motion. This motion constitutes heat, they now understood. Heat is no substance, no fluid, no “phlogiston”—just the motion of molecules.
Individually the molecules must be obeying Newton’s laws—every action, every collision, measurable and calculable, in theory. But there were too many to measure and calculate individually. Probability entered the picture. The new science of statistical mechanics made a bridge between the microscopic details and the macroscopic behavior. Suppose the box of gas is divided by a diaphragm. The gas on side A is hotter than the gas on side B—that is, the A molecules are moving faster, with greater energy. As soon as the divider is removed, the molecules begin to mix; the fast collide with the slow; energy is exchanged; and after some time the gas reaches a uniform temperature. The mystery is this: Why can the process not be reversed? In Newton’s equations of motion, time can have a plus sign or a minus sign; the mathematics works either way. In the real world past and future cannot be interchanged so easily.
“Time flows on, never comes back,” said Léon Brillouin in 1949. “When the physicist is confronted with this fact he is greatly disturbed.”♦ Maxwell had been mildly disturbed. He wrote to Lord Rayleigh:
If this world is a purely dynamical system, and if you accurately reverse the motion of every particle of it at the same instant, then all things will happen backwards to the beginning of things, the raindrops will collect themselves from the ground and fly up to the clouds, etc, etc, and men will see their friends passing from the grave to the cradle till we ourselves become the reverse of born, whatever that is.
His point was that in the microscopic details, if we watch the motions of individual molecules, their behavior is the same forward and backward in time. We can run the film backward. But pan out, watch the box of gas as an ensemble, and statistically the mixing process becomes a one-way street. We can watch the fluid for all eternity, and it will never divide itself into hot molecules on one side and cool on the other. The clever young Thomasina says in Tom Stoppard’s Arcadia, “You cannot stir things apart,” and this is precisely the same as “Time flows on, never comes back.” Such processes run in one direction only. Probability is the reason. What is remarkable—physicists took a long time to accept it—is that every irreversible process must be explained the same way. Time itself depends on chance, or “the accidents of life,” as Richard Feynman liked to say: “Well, you see that all there is to it is that the irreversibility is caused by the general accidents of life.”♦ For the box of gas to come unmixed is not physically impossible; it is just improbable in the extreme. So the second law is merely probabilistic. Statistically, everything tends toward maximum entropy.
Yet probability is enough: enough for the second law to stand as a pillar of science. As Maxwell put it:
Moral. The 2nd law of Thermodynamics has the same degree of truth as the statement that if you throw a tumblerful of water into the sea, you cannot get the same tumblerful of water out again.♦
The improbability of heat passing from a colder to a warmer body (without help from elsewhere) is identical