Saturday, May 1, 2021

Maxwell’s Demon And The Physics Of Information.

From Quanta Magazine, April 22

The thorny thought experiment has been turned into a real experiment — one that physicists use to probe the physics of information.

The universe bets on disorder. Imagine, for example, dropping a thimbleful of red dye into a swimming pool. All of those dye molecules are going to slowly spread throughout the water. Physicists quantify this tendency to spread by counting the number of possible ways the dye molecules can be arranged. There’s one possible state where the molecules are crowded into the thimble. There’s another where, say, the molecules settle in a tidy clump at the pool’s bottom. But there are uncountable billions of permutations where the molecules spread out in different ways throughout the water. If the universe chooses from all the possible states at random, you can bet that it’s going to end up with one of the vast set of disordered possibilities.

Seen in this way, the inexorable rise in entropy, or disorder, as quantified by the second law of thermodynamics, takes on an almost mathematical certainty. So of course physicists are constantly trying to break it.

One almost did. A thought experiment devised by the Scottish physicist James Clerk Maxwell in 1867 stumped scientists for 115 years. And even after a solution was found, physicists have continued to use “Maxwell’s demon” to push the laws of the universe to their limits.

In the thought experiment, Maxwell imagined splitting a room full of gas into two compartments by erecting a wall with a small door. Like all gases, this one is made of individual particles. The average speed of the particles corresponds to the temperature of the gas — faster is hotter. But at any given time, some particles will be moving more slowly than others.

What if, suggested Maxwell, a tiny imaginary creature — a demon, as it was later called — sat at the door. Every time it saw a fast-moving particle approaching from the left-hand side, it opened the door and let it into the right-hand compartment. And every time a slow-moving particle approached from the right, the demon let it into the left-hand compartment.

After a while, the left-hand compartment would be full of slow, cold particles, and the right-hand compartment would grow hot. This isolated system would seem to grow more orderly, not less, because two distinguishable compartments have more order than two identical compartments. Maxwell had created a system that appeared to defy the rise of entropy, and thus the laws of the universe.

“He tried to prove a system where the entropy would decrease,” said Laia Delgado Callico, a physicist at King’s College London. “It’s a paradox.”

Two advances would be crucial to solving Maxwell’s demon. The first was by the American mathematician Claude Shannon, regarded as the founder of information theory. In 1948, Shannon showed that the information content of a message could be quantified with what he called the information entropy. “In the 19th century, no one knew about information,” said Takahiro Sagawa, a physicist at the University of Tokyo. “The modern understanding of Maxwell’s demon was established by Shannon’s work.”....


And from Emanuel Derman:
If you know Maxwell’s equations for electromagnetic fields, can you see that there must be waves? 

Yes that Emanuel Derman
Emanuel Derman On Tokyo and Jetlag And Other Stuff
Here's our boilerplate introduction to what I've come to think of as Dermanettes:
...Today we visit Emanual Derman whom I once described, back when he was blogging at Reuters, thusly:
Mr. Derman is a blogger based in New York City.
He also teaches at Columbia.
Before that he was head of the quantitative strategies group in the equities division, and then head of quantitative risk strategies at Goldman Sachs
And before that he was a theoretical physicist.

I hate him....
Here is his personal homepage.

...Psst...I don't really hate him.
But do visit his homepage to see why one could.....


Readers who have been with us for a while may remember some of our posts on Claude Shannon:

The Bit Bomb: The True Nature of Information
The subject of this article, Claude Shannon has a couple interesting connections to finance/investing/trading beyond 'just' creating information theory (along with MIT's Norbert Wiener who was coming in on a different angle of attack), more after the jump.
Both Aeon and Climateer are reposting, "The Bit Bomb" first appeared at Aeon on August 30, 2017 and graced our pages over the Labor Day weekend, September 3, 2017

"How Information Got Re-Invented" 

"Claude Shannon, the Las Vegas Shark" 

"How did Ed Thorp Win in Blackjack and the Stock Market?"