alxm said:
Now tell me what in the above you disagree with, instead of constructing straw-men and pretending you're the only one here who knows about information theory and thermodynamics?
Of your entire post, this is basically the only sentence I disagree with- I know hardly any thermodynamics, and even less about information theory.
Let's construct a machine which can directly convert information into work. There will be apparent paradox, the resolution of which may shed some light on the interrelationship between information and free energy (and entropy).
You and I sit opposite each other, in thermal equilibrium at temperature T. You have a box, full of gas at temperature T, with a partition in the middle. There are N particles of gas in the whole box (N/2 on each side). I send you a binary message, N/2 bits long, encoded with the following information:
If the bit is '0', take a particle from the left side and move it to the right. If the bit is '1', do nothing.
After receiving my message, you have a copy of the message and you give me the box.
But we are not done- we are not yet returned to our starting configuration. There are a few ways to go back- one by simply reversing the steps (you send me the code and I move the particles), another by me allowing the gas to re-equilibrate (either purely dissipatively, or by letting the gas do some work, or perhaps some other method)- but regardless of what happens, we must somehow end up in our starting configuration. Reversing ourselves is boring. More interesting is what I can do with the box of compressed gas.
Here's the apparent paradox: it seems that I can send two messages with the same entropic quantity of information (all '0' or all '1'), and have two different results: if the message is all '0', the gas is fully compressed and I can extract work from it. If the message is all '1', the state of the gas is unchanged and I cannot extract work.
The solution to this paradox lies in the way the information and state of the gas are related. Moving a particle means you performed a measurement on the location of the particle, whereas doing nothing did not require a measurement.
After you had processed the message by moving particles, if you did not forget the message, you now have *two* copies of the information- one is the information in your memory, the other is the distribution of particles in the box. When I allow the gas to re-equilibrate, I have destroyed a copy of the information, consistent with letting the free energy of the gas within the box dissipate. Only then are we back to the starting configuration (to within a parity transformation): you have a single copy of the message, I have a box of gas with N/2 particles per side. In this way, the paradox is similar to Szilard's engine.
Now let's say you forgot the message after moving the particles. Then, when I allow the gas to do work, we are left with *zero* copies of the message: information has been irreversibly converted into work (or heat).
In terms of a heat engine, by taking free energy from a 'hot' source (reading the message) and then deleting the message (the 'cold' reserviour), work can be extracted.
