what's wrong with entropy?

[scruffy]

We can begin with these three observations:

1. The existence of a bit is information.

2. The state of a bit is information.

3. The probability of transitions between states is information.

These are three distinct and separable types of information.

Information theory only accounts for one of them.

Proposal: the Second Law is misleading. It suggests changes to configurations (order vs disorder), whereas what's really happening is an increase in the number of possible paths (which is a restatement of the idea that "the universe is expanding").

As the universe expands, it takes more yes/no questions to get an answer. For example - you have a bottle of perfume in the corner of an 8x8 room, and 2 minutes after you open the bottle you want to know where one of the perfume molecules is. But during those two minutes your room has expanded, it's now 9x9. So now you need "more" than 6 bits to locate the molecule.

If you didn't know about the expansion, you'd still be asking the 8x8 question, which would give you an incorrect and meaningless answer.

 

[Sherlock Holmes]

We can begin with these three observations:

1. The existence of a bit is information.

2. The state of a bit is information.

3. The probability of transitions between states is information.

These are three distinct and separable types of information.

Information theory only accounts for one of them.

Proposal: the Second Law is misleading. It suggests changes to configurations (order vs disorder), whereas what's really happening is an increase in the number of possible paths (which is a restatement of the idea that "the universe is expanding").

As the universe expands, it takes more yes/no questions to get an answer. For example - you have a bottle of perfume in the corner of an 8x8 room, and 2 minutes after you open the bottle you want to know where one of the perfume molecules is. But during those two minutes your room has expanded, it's now 9x9. So now you need "more" than 6 bits to locate the molecule.

If you didn't know about the expansion, you'd still be asking the 8x8 question, which would give you an incorrect and meaningless answer.

 

[scruffy]

I found a paper which discusses a small part of this at the quantum level (only).

It identified three types of mutually incompatible quantum information.

https://quantum.phys.cmu.edu/QCQI/tqi14.pdf

 

[scruffy]

So, so far, there are at least 6 kinds of mutually orthogonal information:

1. The existence of a thing
2. The states of the thing
3. The probabilities attached to (2)
4. The available configurations for sets of things
5. The probabilities attached to (4)
6. The occupation of states in (4)