[jbay808]

The way to make sense of entropy is to treat it as a subjective quantity. A subjective quantity is a function where the observer's state of knowledge is one of the input arguments.

The article describes it as a measure of hidden information in a system, which is a good description. But that's not a property of the system itself, it's a property of the observer, from whom the information is hidden.

So different observers with different information about a system will have different opinions about its entropy.

My password, for example, to me has zero entropy. I know its microstate. But it's quite secure from someone trying to guess it, and they will think it's quite high in entropy.

If all you know about a system is that it's a kilogram of air at room temperature, it will seem quite high in entropy to you, as many possible microstates are consistent with that description. But if you have godlike knowledge of the exact configuration of every particle in the container, it will seem very low in entropy to you, and that's more than just an accounting difference. Indeed you can use that information to operate a Maxwell's demon and turn the system into a heat engine, splitting the cold and hot molecules into separate spaces and extracting work as though the system really had low entropy to start with. Because it did. To you.

Most of the confusion about entropy comes from what Jaynes calls the mind projection fallacy: the tendency to treat our uncertainty about a system as a property of the system, rather than a property of ourselves.

[alimov]

> The article describes it as a measure of hidden information in a system, which is a good description. But that's not a property of the system itself, it's a property of the observer, from whom the information is hidden.

Was hoping to see someone point this bit out.. I wish references to entropy included this piece of information more frequently. When I was first trying to understand the concept I kept thinking of it as something objective, but as you say it’s a property of the observer

[brabel]

Speaking of observers always rubs me off the wrong way... I don't want to touch on the observer problem, but just to mention something that should be obvious: there's ALWAYS hidden information in any system where time exists. Any "observer" can only know what the world looks like within its light cone. Because quantum mechanics shows that determinism is not possible, it's not possible for any "observer" to know the exact future state of the world outside what was observable within its light cone up until that moment. There's also the problem that you can only store a limited amount of information even given perfect theoretical storage... hence again, some information must be forgotten by whatever the "observer" is... talking about a "perfect observer" that knows all there is to know makes absolutely no sense.

[alimov]

Since entropy seems to be a measure of our ignorance, then there maybe there is no point in discussing a perfect observer (of something that is boundless). Edit: > talking about a "perfect observer" that knows all there is to know makes absolutely no sense.

if there was such a thing as a perfect observer, let’s say it is you, then you would still choose to measure some things, but not others. Unless by “perfect observer” you are referring to something that knows the states of all things simultaneously at all times, in which case that (to me) doesn’t sound like an observer at all, would just be someone/something that knows. So like you said “there is always hidden information” but that information is hidden to someone that is doing the observing and so is dependent on them. Otherwise from what or whom would the information be hidden? What would information even be without an observer?

[rytill]

Whatever is the driving factor behind the laws of physics seems to have “perfect information”. Not implying anything religious.