Ludwig Boltzmann: The Master of Disorder

The principle in physics called entropy has a convoluted history. The genesis of the idea started in the 1800s with the industrial revolution and the advent of steam engines. Although steam power was producing an incredible amount of energy and transforming societies, the fundamental physical laws behind the process was largely unknown. The full story behind solving this question concludes with Austrian physicist, Ludwig Boltzmann, and his view of entropy. His insights into the physical reality behind heat and energy were later applied to a much larger scheme, including the whole universe.

The Universe in a Coffee Cup

Why does a hot cup of coffee left on a table get colder over time? The answer to this simple questionis at the heart of Boltzmann’s idea. The explanation is due to the behavior of atoms. Today, the existence of atoms is taken for granted, but back in the late 1800s many prominent scientists did not believe in atoms (including Ernst Mach, one of Boltzmann’s adversaries). No one had observed an atom, and it was thought that no one ever would. Nevertheless, Boltzmann peered deeper into the physical world than any of his contemporaries.

Let’s get back to the hot cup of coffee. The heat from the coffee will disperse to the cup, the table and the surrounding air, until the temperature of the coffee is roughly equal to its environment. The same amount of energy still exists, but now covers a wider area. The flow of energy, left alone, will always flow from a hot source to a cold source. This natural flow of energy was the secret behind the steam engine, as the heat energy was converted to physical work. Boltzmann realized that this phenomenon of heat transferring and dispersing could be explained within the framework of atoms.

In the hot coffee, the atoms are tightly arranged and jostling about. The vibrations of the atoms are responsible for the heat. But as they move they contact the atoms of the cup, and transfer some of their energy. This continual process of bumping eventually distributes the heat energy to a much larger number of atoms. In the hot coffee the atoms are arranged in a unique way, but there are may possible arrangements in which the atoms can spread out. In the language of entropy, the system has moved from low entropy (an ordered state) to high entropy (a disordered state). The natural tendency for systems to move from order to disorder is now understood as a fundamental principle that underpins the entire universe. Loosely speaking, this describes the second law of thermodynamics.

What is Order and Disorder?

Classical physics, the method of scientific reasoning that held sway since Issac Newton, demanded that precise calculations were made. Physics was about discovering exactly how things moved and interacted. If atoms really existed, the sheer amount of them imposed an almost insurmountable problem. How could they ever be studied? Boltzmann took a different approach. Perhaps his greatest insight was that the motion of atoms could be described mathematically by using statistical probabilities. In addition to studying atoms, probabilities could be used to determine the amount of entropy in any system. This idea leads us to a definition of order and disorder:

Order means that there are very few configurations, if changed, which would go unnoticed.

Disorder means that there are many configurations, if changed, which would go unnoticed.

For example, take the analogy of a deck of playing cards. Dealt at random, there are few arrangements of cards that will line up in numerical order. Conversely, there are many arrangements of cards that will be mixed up. The reason is obvious. The probability is much higher for a disordered configuration than for an ordered configuration. Order is a special and unique condition, while disorder can come about in numerous ways. Therefore, we can conclude that high entropy (disorder) is a more natural state. We can still create order, but we need to intervene in some way. Still, any system left alone will move from order to disorder (or entropy will increase).

Statistical Reasoning

The entropy in a cup of coffee will tend to increase. Someone has to create the order by heating up the water and making the coffee. What would be the likelihood that the heat would naturally occur in the coffee? Of course we know that doesn’t make any sense. Thus by statistical reasoning, it makes perfect sense that disorder is more likely than order. Entropy, and in turn the second law of thermodynamics, is based on the probability of how any physical system will evolve. Eventually, everything dissolves, crumbles, decays, degrades and collapses.

We don’t need to look any further than our own homes, as it is a constant effort to maintain order (the special condition where items are neatly arranged). Disorder happens much more naturally, because there are many more ways in which the home can be disordered. Left unchecked, dirty dishes will accumulate, laundry will build up, and things will get scattered. The condition of the home’s structure will also degrade over time. This is all due to the principle of entropy.

A Story of Triumph and Tragedy

Boltzmann’s theories were highly controversial in his time; many prominent physicists rejected his ideas. And to make matters worse, he suffered from severe bouts of depression (probably due to undiagnosed bipolar disorder). On the positive side, he also went through periods of intense creativity. Aside from describing what entropy actually was, Boltzmann was able to put numbers to his theory. He devised a mathematical formula that could calculate the amount of disorder in a system.

His use of probabilities went against years of certainty behind the theories of classical physics. In the early 20th century, scientists would soon find his method useful in probing the atom. Probabilities would become a fundamental feature of quantum mechanics. The sad part to the story is that Boltzmann’s achievements would only be recognized after his death. In 1906, he committed suicide during one of his episodes of depression. Whether the final blow was delivered by his mental illness or the lack of recognition for his work is unclear. Nevertheless, his lasting legacy is engraved on his tombstone in Vienna: his equation for quantifying entropy, S = K log W.

References: Order and Disorder the ENERGY – HD Documentary, Published on June 24, 2014.