During the second half of the nineteenth century Ludwig Boltzmann changed
thermodynamics forever. He recast it in terms of probability theory.
The behavior of heat and gases reflected reliable trends among masses
of particles impossible to track individually. Inspired by Darwin's idea
of natural selection leading to change over time, Boltzmann's work verified
the theories and observations from classical macroscopic thermodynamics:
things changed in the direction of the more probable. Indeed, the tendency
for atoms to jumble and their intricate patterns to be reduced to ruin
seemed to give inhabitants in this universe—a
kind of cosmic casino—their sense of passing time. A great breakthrough,
Boltzmann's unification of classical thermodynamics with Newtonian
mechanics provided a scientific basis for the perception of linear
time.
Practical, Promethean, and based on observation, classical thermodynamics
was a kind of glorified engineering, stoked by humanity's ancient quest
to master fire. Statistical thermodynamics, predicting the behavior of
masses but not individual particles, placed the observational science
on firmer mathematical footing. In doing so it increased its explanatory
power, broadening it to treat gases and other phenomena.
Boltzmann thus applied probability theory to matter's tendency to come
to equilibrium. He recognized the power of statistics to deal with intractably
large numbers and that, with enough cases, the ideal and the real converged.
If one wanted to know the chance of heads or tails from a perfectly balanced
coin, for example, the average behavior would be apparent only after
many flips of the coin. Only when we have flipped the coin a huge number
of times will the distribution approach 50% heads, 50% tails. But when
one is dealing with 1023 molecules, statistical averages converge with
reality: there are so many particles that their average aggregate behavior
is indistinguishable from their actual aggregate behavior.
Despite being rather majestic—Boltzmann's deep integration of
probabilities into science was adopted by quantum mechanics—it
was attacked from the start. The most basic line of attack at the time
of Boltzmann's formulation of a statistical interpretation of thermodynamics
was his use of the never-before-seen-or-measured microscopic "atoms
of molecules." Remember Boltzmann advanced his ideas some fifty
years before the recognition of atoms by scientists such as Sir J. J.
Thomson and Lord Rutherford. Boltzmann's critics were formidable, the
finest physicists in Europe at the time. Max Planck (who devised the
version of the entropy equation engraved on Boltzmann's tombstone), Ernst
Zermelo, Ernst Mach, and Friedrich Wilhelm Ostwald attacked Boltzmann
relentlessly—not because he viewed time as one-way, but because
he had the audacity to suggest matter was made of atoms. This group became
known as the Vienna Circle of "logical positivists" and insisted
that science could be conducted only when all the objects of study were
seen and understood. Their main objection to Boltzmann was that there
was no means of verifying the existence of atoms and molecules, whose
behavior lay at the foundation of Boltzmann's probability-based vision.
A German student described a debate between Ostwald and Boltzmann at
the Lübeck Scientific Conference in 1885. "The fight between
Boltzmann and Ostwald was like the fight of a bull with a supple fighter.
But this time the bull overcame the torero in spite of all his art in
fencing. The arguments of Boltzmann won. We younger mathematicians were
all on Boltzmann's side" (Coveney and Highfield 1991, 175).
On September 5, 1906, while on a rest holiday on the Adriatic coast,
Boltzmann committed the irreversible act of suicide. Only one year before,
Einstein had published his work on Brownian motion and microscopic thermal
kinetics. Brownian motion can be seen under a microscope as the incessant
jostling of tiny (one micron or smaller) particles suspended in water.
The particles are agitated by something even tinier in the water—atoms. This work
by Einstein provided the "proof" for the kinetic theory of heat—the
unseen atoms could now be seen, skittering and grazing about, bumping up
against larger particles.
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Part
I: The Energetic
1. The Schrödinger Paradox
2. Simplicity
3. Eyes of Fire: Classical Energy
Science
4. The Cosmic Casino: Statistical Mechanics
5. Nature Abhors a Gradient
6. The River Must Flow:
Open Systems
7. Too Much, Not Enough: Cycles
Boltzmann recast thermodynamics in terms of the
statistical distribution of energy microstates within a system. To understand
microstates, consider marbles in interconnected small boxes contained
within a large box called a macrostate. Consider a box with ten thousand
marbles in one of ten equal-sized compartments with the rest of the compartments
empty. If doors are opened between all the compartments and the box is
subjected to a long-term pattern of random shaking, one would expect,
over time, to see a distribution of about a thousand marbles, behaving
like gas molecules, per compartment. This randomization of the molecules
to the equiprobable distribution corresponds to the macrostate with the
maximum entropy for the closed system. If you continued the shaking it
would be highly, highly improbable—but not impossible—for all the
marbles to reseparate themselves into the low-entropy configuration with
ten thousand marbles in a single compartment. In the same way, it is
not impossible that all the oxygen atoms in your bedroom will congregate
in a corner, gagging you; but the chances are so minute, the improbability
so huge, that you need not worry….
Maxwell's demon is a thermodynamic thought experiment.
James Clerk Maxwell imagined a small, nimble-fingered, informed entity
(the demon) that could discriminate between fast-moving "hot" molecules and slower "cooler" molecules.
The demon would open a trapdoor and allow only the fast-moving molecules (squares)
into one side of the chamber; the slower molecules (circles) would be segregated
in the other side. This scheme was accomplished using no work. If possible, such
a concept would defy the second law, as it would create a gradient, from which
work could be extracted, out of nothing.
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