Charles Liu

Yes.

Did I do it right?

Yes, Neil is precisely correct.

And so the stuff that's hidden, that information underneath, right, that actual specific coin flips, and then the actual result information that you want, how many heads, how many tails, that difference could be said to be the entropy of the system that you don't see when you're getting the information out of the flips.

Yes, absolutely.

This happens when we boil water, for example.

When you're trying to turn water from liquid to gas on your stove.

What happens is that it stops at 100 degrees Celsius, right, a standard boiling temperature for a period of time.

And then the steam that comes off is still 100 degrees Celsius, but it has so much more entropy.

It has so many more possible states of the individual atoms moving around compared with the liquid versions.

It's not a matter of how far apart they are.

It's a matter of how much freedom each particle has.

How much freedom they have moving inside of it.

That's right.

Right, right.

And so in order to compensate for that, you have to heat the water up extra.

You don't change the temperature, but you're changing the amount of energy inside because of the entropy increase that you have to put in in order to turn it into gas.

Yeah, superb question.

And in fact, I will say that that is actually a problem for astronomers sometimes.

We don't know whether or not the object's colors are caused by, or the redshift,