8 ms·

I've heard this explanation alluded to, but I've never understood the details. What does the last sentence mean?

dvt 5y ago
> What does the last sentence mean? "Waste" here means entropy. So the "thinking" that the demon does actually increases the entropy overall. In other words, even though the system's entropy seems to be decreasing (since particles are being neatly sorted), the process used in the sorting must create some kind of random garbage that actually will be a net increase in entropy, in spite of the now-sorted particles.
ncallaway 5y ago
Basically, any temperature difference between two regions of space can be used to do Work* (essentially, there is a maximum amount of Energy that you can extract from that temperature difference to do anything with). If everything in your closed system is the same temperature, then there is no Energy that you can capture in order to do Work. Well, if we have this demon that can open this gate at _just_ the right times so that it can separate hotter particles from colder particles, then it is able to _create_ a temperature difference where there wasn't one. So, this demon would allow us to use our closed system to do an infinite amount of Work. It would act as a sort of perpetual motion machine. - Step 1: Let the demon open the gate at the right times to separate the hotter gasses (more energetic individual particles) from the colder gasses (less energetic individual particles). - Step 2: Replace the barrier/gate with a heat engine, and let the natural flow of energy from hot -> cold, drive our heat engine and push the box. - Step 3: Once the temperature has diffused enough that our heat engine can no longer do any productive Work (that is, the temperature has equalized), then we replace the heat engine with the barrier/gate and let the demon go back to work. That sets us up to discuss the final sentence. With the advent of information theory, we now know that there is a _minimum amount_ of Work that a hypothetical demon would need just to know when to open and close the gate. That Work requires Energy to perform. As it happens, that Work that the demon must do requires more energy than the demon is able to create by separating the particles. Which means the closed system of particles + demon will still increase entropy, because the demon _consumes more energy than it creates_. Basically, we were able to do the math about the theoretical limits of a perfect demon, and if you were able to make one it doesn't break the 2nd law of thermodynamics. The reason this stumped scientists for a long time is we didn't have the ability to calculate the _minimum amount of Energy_ that would be needed by the demon's brain. * Work here being the physics concept of work. For example, we could move a box around by using a heat engine to turn the temperature difference into adding a physical force to the box.
- drran 5y ago
  We can use potential barriers to separate hot and cold molecules, e.g. water pool <-> water surface (barrier) <-ambient heat-> vapor <-> condensator <-> water <-> hydroelectric powerplant <-> water pool

dvt 5y ago

> What does the last sentence mean? "Waste" here means entropy. So the "thinking" that the demon does actually increases the entropy overall. In other words, even though the system's entropy seems to be decreasing (since particles are being neatly sorted), the process used in the sorting must create some kind of random garbage that actually will be a net increase in entropy, in spite of the now-sorted particles.

ncallaway 5y ago

Basically, any temperature difference between two regions of space can be used to do Work* (essentially, there is a maximum amount of Energy that you can extract from that temperature difference to do anything with). If everything in your closed system is the same temperature, then there is no Energy that you can capture in order to do Work. Well, if we have this demon that can open this gate at _just_ the right times so that it can separate hotter particles from colder particles, then it is able to _create_ a temperature difference where there wasn't one. So, this demon would allow us to use our closed system to do an infinite amount of Work. It would act as a sort of perpetual motion machine. - Step 1: Let the demon open the gate at the right times to separate the hotter gasses (more energetic individual particles) from the colder gasses (less energetic individual particles). - Step 2: Replace the barrier/gate with a heat engine, and let the natural flow of energy from hot -> cold, drive our heat engine and push the box. - Step 3: Once the temperature has diffused enough that our heat engine can no longer do any productive Work (that is, the temperature has equalized), then we replace the heat engine with the barrier/gate and let the demon go back to work. That sets us up to discuss the final sentence. With the advent of information theory, we now know that there is a _minimum amount_ of Work that a hypothetical demon would need just to know when to open and close the gate. That Work requires Energy to perform. As it happens, that Work that the demon must do requires more energy than the demon is able to create by separating the particles. Which means the closed system of particles + demon will still increase entropy, because the demon _consumes more energy than it creates_. Basically, we were able to do the math about the theoretical limits of a perfect demon, and if you were able to make one it doesn't break the 2nd law of thermodynamics. The reason this stumped scientists for a long time is we didn't have the ability to calculate the _minimum amount of Energy_ that would be needed by the demon's brain. * Work here being the physics concept of work. For example, we could move a box around by using a heat engine to turn the temperature difference into adding a physical force to the box.

drran 5y ago
We can use potential barriers to separate hot and cold molecules, e.g. water pool <-> water surface (barrier) <-ambient heat-> vapor <-> condensator <-> water <-> hydroelectric powerplant <-> water pool