Heat and Information

[Vkothii]

I decided to get carried away and ghost this:

Temperature is an interval.
Heat is curvature, or change in curvature over time.
Entropy is volume.
These all have dimension, which we can fix, or set.

A message is an interval.
Information has curvature or change (a pattern).
Information entropy is a volume.
These have no dimension, so we don't fix or set them. They are scalable, whereas heat is a scale.

There's a zero-point temperature, so zero-curvature, and zero-volume.
But not with information, it doesn't have a zero-point, it is a zero-point + a one-point. Like a sort of gap with no 'size'.

To understand either, I claim that you need to understand both: Thermodynamics and Information Theory.
Or at least the way entropy is defined in either, which would require a few fundamentals to be grasped (non-trivially).

How about the Physics/Math jocks?

For starters:
Information entropy has an algebra, or it's the matrical view: you get a matrix; thermodynamic entropy has a geometry, it has a topology as well. How do you visualise the topology or geometry of a matrix?

Pedantic note #1: the "+" symbol doesn't always mean "add". There's more than one symbol definition for that one.

[Vkothii]

Alrighty, under the radar, then.

It's where I live anyway.

[Vkothii]

But, for example, it means there's an informational equivalent of heat.
And for anything else with curvature and volume, like gravity and electromagnetism. And black holes.

[Reiku]

Curvature... i'm assuming you are referring to mathematical probability curves?

[Enmos]

Is there a correlation between temperature and information ?

[Vkothii]

You've seen the eqns for entropy and enthalpy?

How about for conditional or Shannon entropy?

With information having curvature, it isn't like the usual idea - but it is still conceptually a volume, and a volume can have a surface, a surface can have curvature.

[BenTheMan]

Entropy is volume.

But Hawking showed that entropy scales like the surface of an object, not the volume.

[Vkothii]

But Hawking showed that entropy scales like the surface of an object, not the volume.

So you're saying heat can be scaled, in terms of the surface area of some object that has a volume of heat? Or you mean information has a scale that is equivalent to a surface area?

[BenTheMan]

Well, the analogy between information and entropy is correct. The Entropy of a black hole goes like the area of its horizon, and because "black hole" is as dense as it gets, the bound on the entropy that lives in a volume of spacetime is bounded by its surface area, and NOT its volume. This is counter-intuitive, because (classically at least) we'd expect the number of states available to the system to scale like the volume.

I have to say, most of your original post is incomprehensible, and I almost moved this to pseudo-science. I see no basis for claims like "Heat is curvature"----well, I DO see one basis, but I'm not sure that it's valid. But I'm no expert in GR.

[Vkothii]

How would a PhD student describe the "energy" a body has, in terms of the sum of all motions of small molecules that it's made of, then?
We call it heat content (in some textbooks), how then is the content of something usually expressed if not as a volume?

Or is that a bit incomprehensible?

And you haven't convinced me that this:

The Entropy of a black hole goes like the area of its horizon, and because "black hole" is as dense as it gets, the bound on the entropy that lives in a volume of spacetime is bounded by its surface area, and NOT its volume.

is a show-stopper. What is the significance? I can't see it, so please elucidate. (IOW - what the hell is the significance)?

Is there some big paradox or something, with having to describe entropy as an area, not a volume, for black holes? Does that mean we can't describe it as a volume for objects that are not black holes, or we have to start again?

[temur]

You are talking about heat content, Ben is talking about entropy (or information) content, capish.

[Vkothii]

No, I'm talking about heat and information - both of these have a curvature and an area and also a volume.

I'm sorry, but they just do. What do you think I can do about it?


P.S. I'm not actually sure what Ben is talking about, tbh.
That one's been pushed on to the stack for now, I await the required de-stacking operator.

[temur]

since they are different things, you should consider them separately when it is necessary.

[Vkothii]

Well, I do.

I know, for instance, that heat is a name we give to something that objects can have, inside them, on their surface, and "outside" (you can feel something without touching an object, like from a distance).

[Vkothii]

So, who'd like first dibs on what they know information is? Is there a Ph.D. student version?

Here's the undergrad version (off the top):

Information has only two possible states: 1 and 0. These are not literally "one thing", and "zero things", they are just symbols that represent the available states in information.

Information can be physical - like these symbols I'm typing have a physicality, or a representation in the states of transistors in a memory chip, in a CPU, along a wire encoded in some form (usually as strings of a nominal length, often a power of 2).
Information is binary; that means it isn't unitary, or trinary, or another kind of -ary.
A string of 1 and 0 symbols is generally called a message. Messages have an information content that depends only on other messages and their content.

Any physical or abstract value can be represented as a string of 1s and 0s, or bits.

And now, this:
"...all physical systems are computers. Rocks, atom bombs, and galaxies may not run Linux, but they too register and process information. Every electron, photon and other elementary particle stores bits of data, and every time two such [computers] interact [(communicate)], those bits are transformed. Physical existence and information content are inextricably linked, "
--Seth Lloyd & Y. Jack Ng, Sci Am Nov 2004

[temur]

What do you mean by PhD student version? Is your version high school student version or professor version?

[Vkothii]

Have another squiz, cobba.

P.S. Some more incomprehensibility:

Information has energy or mass (physical information is energy or mass).
Heat does not have mass or energy. Heat is energy, it has a mass equivalent.
Information can be either. Or it can be neither (an abstraction).

[temur]

You lost me.

[Vkothii]

There you go.

Ok, try this one:
can you explain how superposition and interference are connected? Interference in general is what occurs when there is more than one possible result, or outcome (as in tossing a coin, or mixing waves together).
What is the informational view of these phenomena?

[Vkothii]

Since there's a graduate student here who has said: "I see no basis for the claim that heat is curvature", maybe I should leave that part out and just say: temperature is an interval (or is it something else?), entropy is an integral, which can be a volume (or that's pseudoscience too?).

But, if entropy can be a volume, or an area, and temperature is in fact an interval, why does an area or a volume not have a curvature, or what is heat then?

I'd really like to know how to get from an interval on some line, to a volume or area without seeing curvature of some kind (maybe I should enrol in a calculus class)?