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Comment by zug_zug | Hacker News Reader

There's something about attempts at entropy that feels entirely inadequate.

The definition of "law" in science isn't something that's true, just something that we haven't observed any exceptions to (yet). However entropy, is in larger systems entirely unmeasurable as far as I understand (is there even a unit for it?).

Rather than tackle-these scientific shortcomings head-on, most tend to gloss over it. Perhaps a good place to start is to talk about the limited places we can observe it, and the logical reasons that our observations in these limited places must apply more generally. And then to explain whether a unit exists or not, why it matters so much.

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Entropy is a measure of the uncertainty that an observer has over the microstates (i.e. the exact state of every atom) given their knowledge of the macrostate (i.e. what they are capable of describing: like "the water is just above freezing"). So it's inherently a subjective concept. The most common unit for entropy is the bit, same unit as information.

Anyway, entropy is measurable just like any other physical quantity. You need to determine what your model of the microstates is (often an "ideal gas", with independent molecular point particles with their own positions and velocities, and all interactions are perfectly elastic collisions), what you currently know (stuff like type of gas, pressure/volume/temperature), and then there is a clear answer to what the entropy is.

The true law underlying the second law of thermodynamics is conservation of information. In (classical) physics, this is typically cast as Liouville's theorem, which shows that the area of the phase space of a system must remain constant. (In quantum, it's only true for unitary transformations, which may or may not be everything depending on your interpretation of QM).

Anyway, if you're curious about learning more, I highly recommend http://www.av8n.com/physics/thermo which is an amazing online (and free) book that clarifies the concepts of thermodynamics brilliantly.

Could you recommend more like that?

Everything on that website is good like that, but unfortunately I wish I had more like it to recommend.

>> Anyway, entropy is measurable just like any other physical quantity

Uh, I measure the mass of a baseball by putting it on a scale, and I get an objective number in kilograms. Similar for velocity, temperature, and volume.

So far as I know, entropy is pretty unique in that there isn't, and will never be an instrument that gives the number of bits in a baseball.

>> So it's inherently a subjective concept.

Yes, this is my point. Almost nothing in physics is subjective.

Yeah, it is different, but once you know what you're after you can measure. It's a "type error" to ask for the number of bits of entropy in a baseball, but if you ask for the bits of entropy of a baseball given everything you know about the baseball (i.e. mass, composition, temperature), then you can measure it. You could even design a special instrument which makes relevant measurements of observable quantities and then calculates the entropy of a given object from those.

Temperature is actually defined from entropy, it's the change in energy per change in entropy. So it too is inherently subjective. One way to think about this is that to a simulator or god outside of our universe, who can precisely see everything happening in the universe, the temperature and entropy of everything is exactly zero (of course, they would be able to predict what we would measure it as). To them, they would see the level of a thermometer as simply a mechanical consequence of all the particles nudging it to that exact place (like you would if you saw someone pump the mercury up the tube -- you wouldn't conclude it must have gotten much hotter suddenly).

> So far as I know, entropy is pretty unique in that there isn't, and will never be an instrument that gives the number of bits in a baseball.

Nonsense. Black Hole entropy is measurable in exactly the same way - put it on a scale, get mass in kilograms, from mass compute radius and area - voila, you've got an entropy

In classical thermo, entropy has units of J/K. It's the gradient of the Helmholtz free energy w.r.t. temperature (at fixed volume). I think experimentally one generally measures the heat capacity as a function of temperature, from which you can obtain the entropy.

I've tackled this problem. Basically most people, even smart people don't understand entropy correctly.

Entropy is not a law. It is a derivation. You can derive entropy mathematically from other axioms we assume are true in reality.

Let me state it plainly in a sentence that is not entirely correct but will help elucidate the meaning of entropy:

Systems tend toward disorder because there are more possible disordered configurations then there are ordered configurations.

This is entropy (sort of).

If your system is a bunch of 6 sided dice one ordered configuration is rolling a 1 on all the dice. Another ordered configuration is rolling a 5 on all the dice. A more likely but ordered configuration is rolling either a 1 or a 2.

There are numerous ordered configurations of a system but the number of unordered outcomes is by far greater then ordered outcomes. If you have a system of dice all facing up with 1s the system is in a low entropy ordered state. If you shake all the dice, it is more likely for the dice to come out in a random state all with random numbers. Shaking the dice is increasing entropy. Entropy increases. But you see here because you relate the dice to probability it's easy to see how by probability the dice should trend toward more disordered states.

The same phenomena goes for particles in a box. Instead of the numbers on the side of the dice replace it with the position of each particle. Shaking the dice is exactly isomorphic to particles traveling in random directions. By probability, dice will roll random disordered numbers just like how by probability randomly moving particles will move into randomly disordered positions.

The same probabilistic intuition that you have for why throwing a bunch of bricks at the ground won't be accident construct a house is exactly the intuition behind probability AND as a result entropy.

The real phenomena here is probability. Why does it apply to reality? We don't know. But entropy is just a consequence of it. Entropy is simply saying (again sort of) systems tend toward more disordered states because disordered states are more numerous and therefore more probable.

The axiom or "law" as you call it is probability and entropy is a theorem or derivation that is a consequence of probability.

This is just a really simple explanation of entropy. Entropy is actually more general then this. It applies even to systems where "ordered" states outnumber "unordered" states. You can see my other explanations in this thread I get into it deeply.

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