[adeledeweylopez]

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.

[zug_zug]

>> 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.

[adeledeweylopez]

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).

[Iwan-Zotow]

> 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

[joycian]

Could you recommend more like that?

[adeledeweylopez]

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