I was hoping the recent spate of threads on information and thermodynamic energy would lead to Maxwell’s demon, Sizlard’s engine,
Landauer and
Bennett.
Will’s explanation is right on, I think: informational entropy isn’t analogous to thermodynamic entropy – it’s precisely equivalent to it. Also, information can’t be considered “metaphysical” or “pure abstraction”, but must be represented in some physical medium. Arguably all sound science supports this view.
Rather than choosing units with a
Boltzmann constant (
) of 1, as Will does, to allow more intuitive examples, I find it helpful to use SI units. For example, erasing this post at room temperature requires a minimum of about
.
This tiny quantity is entirely washed out by the many Joules/second (watts) of any commonplace computing hardware, but is there as a theoretical limit to computer power efficiency.
There’s a lot of history around Maxwell’s demon, early resolutions of the paradox it presented, Sizlard’s resolution of it, and later refinements and modernizations by folk leading up to the defining work of Bennett in the 1980s. The salient feature of this history, IMHO, is that it’s a series of compelling and widely accepted, but disagreeing explanations of the paradoxical nature of information and physical reality. To clearly understand and communicate this history, a clear understanding of the basic design, similarities, and differences of the two engines, Maxwell’s and Sizlard’s, is crucial:
- Both involve a box with a shutter that can be opened and closed. A key assumption is that the shutter can be made to require arbitrarily little work to move as quickly as necessary (well balanced, friction-free, etc), so that it doesn’t require more energy than the engine produces. In both cases, at least one particle (usually described as a gas molecule) is inside the box.
- In Maxwell’s version, a daemon “sees” each particle, calculates its velocity (speed and direction), and opens then closes the shutter as needed. In his description, many particles are in the box, with a typical (Boltzmann) assortment of speeds – though the engine would still work with a single particle. The daemon “sorts” the hotter/faster particles from the slower/cooler ones, creating a heat difference that is used to power the engine. The key feature of Maxwell’s engine is that the daemon detects a particle before moving the shutter.
- In Sizlard’s version, the shutter is opened and closed without attempting to see the particle(s). In his description, a single particle is in the box – though the engine would still work with many particles. The “daemon” – now intuitively imaginable a simple mechanism – determines which half of the divided box the particle is on, and “hooks up” the engines “transmission” as needed. [b]The key feature of Sizlard’s engine is that the daemon detects the particle after moving the shutter[/b\.
Prior to Sizlard’s 1929 explanation, the best accepted explanation’s of Maxwell’s 1867 paradox involved considering what abilities were in principle possible for a “daemon”. The best-accepted conclusion was that, in a system at thermal equilibrium with no unpermitted influx of energy, such as illuminating light, there was no way any possible daemon could see a particle, because the emitted glow of the particle would be indistinguishable from the glow of walls of the box. Looking into a very hot oven (kiln) illustrates this effect – until the walls and contents have cooled slightly (and at slightly different rates), the contents (eg: baked stoneware) are “lost” in the overall glow. An emerging formal understanding of atoms and radiation allowed this explanation to be made well and formally.
In 1912, Marian von Smoluchowski attempted to come up with a design that didn’t need to light-based “seeing”, resulting in a “valve” consisting of a spring-loaded swinging shutter. He then explained why it couldn’t work – a mechanically efficient spring would eventually allow the door to swing at random, doing nothing useful, while any dampened spring would (like the shock absorber on a car) produce heat – never less than it extracted for the engine.
Sizlard’s explanation also didn’t require any light or “seeing” at all – its after-the-action measurement could be done from outside the box with a sensitive scale. Unlike Smoluchowski’s attempt, it works, in principle. All the previous radiation theory explanations were thrown out.
Sizlard, largely intuitive and practical engineer that he was, fumbled the explanation, not realizing the significance of “resetting the bit” at the heart of his “transmission shifting” mechanism. (In his drawings, this bit is usually a little sign with “L” or “R” on it. He appears to have assumed that, like the other parts of the mechanism, this bit could be made to require arbitrarily little energy, and thus ignored it.
Not until 1961 would Rolf Landauer write the formula we’ve been using above (
). He didn’t much stress it or it’s connection to the Maxwell and Sizilard engines, so it wasn’t ‘til Bennett’s 1982 paper that science-literate folk began using his explanation in place of the old “can’t see it” ones. I first encountered it in a magazine article – a 1986-1988 Scientific American, I recall, sitting in a restaurant on my way to the subway on the way home from work, if memory serves me correct, one of those wonderful reading experiences common among we who read science literature.
An important point, I think, is that Sizlard’s engine requires no unexplained “daemon” mechanism. A purely mechanical, “unintelligent” design is possible. The few realistic mechanical drawings I’ve seen feature a lot of balance beams, pivots, and latches, and are based on the idea that you can determine which half of the shutter-divided box the molecule is on by weighing it. Though to the best of my knowledge, no such engine has actually been built, and if one were, it would likely be many orders of magnitude less thermodynamically efficient than the ideal given in Landauer’s formula, it is in principle physically possible – in short, filling some sort of memory with random bits can do physical work in a system at thermal equilibrium.
Most discussions like this thread’s, including Maxwell, Sizlard, and Bennett’s papers, had nice illustrations. Though I’ve searched at some length for the last couple of years for good weblinks to such illustrations, I’ve yet to find one, or draw my own. Here are two good ones, with discussions and histories similar to the above and earlier in this thread:
http://www.aueb.gr/pympe/hercma/proc...ARAYANNI-1.pdf;
Laplaces's Demon and Maxwell's Demon, the Demons of Classical Physics - Numericana.
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My perspective and history of ideas on Maxwell & Sizlard engines and explanations
