Science Forums 2

[CraigD]

The claim

Originally Posted by Shubee

[In chapter 9 “Maxwell’s Demon” of “Mr Tompkins in Paperback”] George Gamow simply recreated the original story of Maxwell's demon by giving it a quantum mechanical twist. That's the meaning of this demon using a tennis racquet. I believe it's clear that my quantum mechanical interpretation agrees perfectly with George Gamow's obvious intent.

appears to me incorrect. Unlike the preceding chapters of Gamow’s book, this chapter contains no references even to the term “quantum”, and shares its title with a well known classical thought experiment.

Shubee, have you any reference to a scientist or any other sort of person sharing you interpretation of this story as having a “quantum mechanical twist”

Though I’ve long enjoyed Gamow’s science popularizing writing (I grew up on it!), IMO he made some regrettable slips in his “Maxwell’s Demon” story.

The essential trait of Maxwell’s demon, as described by Maxwell and in serious treatments of the idea, is that it does arbitrarily little work. The usual description is of a gas-filled cylinder separated by a piston, with a door in the piston that can be quickly open and closed by the demon with arbitrarily little force. The demon opens the door when a faster-moving molecule approaches it from the left moving to the right, or when a slower-moving molecule approaches from the right moving to the left. By sorting faster-moving molecules on the right, and slower-moving ones on the left, while doing an arbitrarily small amount of mechanical work, the demon causes the pressure on the right wall of the piston to be greater than on the left wall, allowing it to move, doing mechanical work in violation of the laws of thermodynamics.

Gamow’s elegantly dressed demon doesn’t do arbitrarily little work. Rather than sorting the gas molecules via a door, it swats them around forcefully with “an instrument like a tennis racket”. This misses the essential character of the thought experiment. If the demon were capable of this sort of molecule-accelerating, he could more easily accomplish his water-boiling trick simply by increasing the speed of every molecule he encountered, adding energy to the system in the manner of an ordinary heating element.

Had I been Gamow’s editor, I would have had him dodge this failing with a bit of elaboration on the demon and his molecule-manipulating instrument. With apologies the late author, my rewrite of the last 500 words of the story:

So saying, Maxwell's Demon left Maud perched on the edge of the ice crystal, like an unhappy mountain climber, and set about his work.

Clinging to an instrument looking like an oversize canoe paddle – though, Maud reminder herself, in reality far smaller than the tiniest bits of barley ash in her husband’s wiskey – with the slightest shift of balance, the Demon dipped its blade into the path of a particular molecule in the turbid roil beneath which sucked it and him end-over-end and down in a seemingly random direction, to carom off another molecule, then another and another, until demon and racquet seemed utterly at the mercy of the chaotic swirl of molecules. Gradually, however, Maud discerned method behind his wild ride. Through subtle tucks of his body, he steered the racquet into the path of the fastest molecules, deflecting them back into the layer beneath her feet, while allowing or even nudging the slower moving molecules to drift quietly deeper, always managing to have the rebound propel him on a course to deliver his next stroke. Despite the fury of the molecules – which, after a few minutes, were clearly more agitated in the layer just beneath the surface than deeper down, and increasingly beginning to snap free of their jostling companions to escape into the less packed expanses above – Maud though “why, he’s hardly putting any effort into it at all. A good thing, too: those pants are really not suitable exercise cloths!”

Molecules were now escaping in groups of thousands together, tearing through the surface as giant bubbles. Then a cloud of steam covered Maud's whole field of vision and she could get only occasional glimpses of the tumbling paddle or the tail of the Demon's dress suit among the masses of maddened molecules. Finally the molecules in her ice crystal perch gave way and she fell into the heavy clouds of vapour beneath. . ..

When the clouds cleared, Maud found herself sitting in the same chair she was
sitting in before she went into the dining room.

'Holy entropy!' her father shouted, staring bewildered at Mr. Tompkins' highball. 'It's boiling!'

The liquid in the glass was covered with violently bursting bubbles, and a thin cloud of steam was rising slowly toward the ceiling. It was particularly odd, however, that the drink was boiling only in a comparatively small area around the ice cube. The rest of the drink was still quite cold.

‘Think of it!' went on the professor in an awed, trembling voice. ‘Here I was telling you about statistical fluctuations in the law of entropy when we actually see one!
By some incredible chance, possibly for the first time since the earth began, the faster molecules have all grouped themselves accidentally on one part of the surface of the water and the water has begun to boil by itself! In the billions of years to come, we will still, probably, be the only people who ever had the chance to observe this extraordinary phenomenon.' He watched the drink, which was now slowly cooling down. 'What a stroke of luck!' he breathed happily.

Maud smiled but said nothing. Out of the corner of her vision, she caught a glimpse of motion in the dining room, and was unsurprised to find herself again in the presence of the elegantly dressed Demon.

“My father does go on so” she said with a touch of exasperation. “all that about luck and billions of years and phenomena. Wouldn’t it just put him in his place if you’d repeat your joke, not a minute after he’s said all that?”

“Alas, madam, that’s not possible,” said the Demon with a regretful shake of his head.

“Why not?” asked Maud, “surely you’re not tired, what with hardly moving a muscle in all that stirring?”

“You’re right – physical effort doesn’t enter into the equation for beings like me. The laws of probability and thermodynamics, though, are not to be denied, no matter what old James Clerk hinted.

“Information is my limitation,” said Maxwell’s Demon. “All of that sorting takes a bit of mental gymnastics, what someday everyone will call computing resources. That little bit of disorder I straightened out in your husband’s drink is all up here now,” he said, tapping his right horn nub, “every little detail of each momentum vector, and needs to be cleaned out before I can play another joke like that last one.

“Surely forgetting all that … data … is less work that memorizing it,” said Maud.

“Not so,” corrected the Demon (who was beginning to sound to Maud as bad as her father). “gaining information is permitted without the introduction of energy into the system. Forgetting – or better put, resetting – is what takes work, of the mundane, mechanical kind. I’m due for a memory wipe as soon as I get home to … wherever it is demons go in their down time. You’ve plenty of mundane energy at hand in the kitchen, but demon etiquette prohibits that sort of borrowing, and even of it didn’t, They don’t let us carry around the paraphernalia for that sort of thing.”

Maud thought she could understand the wisdom behind rules along these lines.