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> It just so happens that in thermodynamics those microstates are the positions and velocities of particles, but that that is a reflection of the underlying phy

> It just so happens that in thermodynamics those microstates are the positions and velocities of particles, but that that is a reflection of the underlying physics. It's not inherent to the definition. Yes, but the rather complicated notion of microstate (or probability or knowledge or information) is not necessary in the thermodynamic definition, which is why it is valuable. > For example, there is this physical phenomenon called specific heat, which makes temperature scales non-arbitrary. If you start by introducing the existence of specific heat (which is a pretty good way to introduce concepts related to temperature both in the statistical and in the thermodynamic case) then you indeed need to choose a canonical temperature scale. Kinda how introducing exponentiation through its derivative provides a canonical choice for the basis of the logarithm. But it is important to appreciate the fact that this canonical choice is somewhat arbitrary: it just makes the equations look more "natural", nothing more. > I'm not pointing this out to challenge your bona fides, only your pedagogy. But I never challenged your assertions on pedagogy. I repeatedly and enthusiastically agreed with them in all my posts. I just strongly disagree with your definition of the word "understand". > You may be right about these things, but you haven't actually defended or supported them. You've just put them out there as bald assertions. I don't see how you expect that to be constructive. Part of it is that I never claimed that understanding entropy is easy. I multiple times referred to the axioms in question by name, but did not claim there is a simple explanation that would let one understand what entropy is. The wiki pages on the topic are quite instructive though: - https://en.wikipedia.org/wiki/Zeroth_law_of_thermodynamics#Foundation_of_temperature https://en.wikipedia.org/wiki/Zeroth_law_of_thermodynamics#F... - https://en.wikipedia.org/wiki/Thermodynamic_temperature https://en.wikipedia.org/wiki/Thermodynamic_temperature - Most importantly, the various statements of the second law. I claim fully understanding entropy requires understanding why these various statements are equivalent: https://en.wikipedia.org/wiki/Second_law_of_thermodynamics#Various_statements_of_the_law https://en.wikipedia.org/wiki/Second_law_of_thermodynamics#V... > Information-theoretic entropy is a generalization of thermodynamic entropy, not a "heuristic". No, they are different concepts, neither one is generalization of the other. That is the point I am making all along. "Password entropy", the way it is commonly used and how I assumed you used it, as in "here is my password, calculate its entropy" is not (information theoretic) entropy, it is just a useful heuristic figure of merit. You can not have entropy without having some probability distribution as you already said in your clarification. And a password is just a single microstate: there is no such thing as entropy of a single microstate, but again, it seems we are in agreement about that. > It just so happens that in thermodynamics the incompleteness of our knowledge is determined by physics whereas. This should say "in statistical physics". Thermodynamic entropy has (superficially) nothing to do with knowledge or information. Few more fun references if you are into extreme mathematical rigor: - https://web.ist.utl.pt/berberan/data/68.pdf https://web.ist.utl.pt/berberan/data/68.pdf - https://en.wikipedia.org/wiki/Constantin_Carath%C3%A9odory#Thermodynamics https://en.wikipedia.org/wiki/Constantin_Carath%C3%A9odory#T... Edit to add: There is a neat "contradiction" between the notions of thermodynamic entropy and statistical entropy. Namely, the notion of ergodicity. Thermodynamic entropy does not let you understand ergodicity or the fact that entropy is permitted to spontaneously drop. Information theoretical approaches do permit you to talk about entropy dropping on its own. While on the topic of pedagogy, discussing this clash is probably quite fruitful. But it is a bit outside my area of expertise. The following is probably a good place from which to start picking terms to google https://math.stackexchange.com/questions/433854/relationship-between-entropy-and-ergodicity https://math.stackexchange.com/questions/433854/relationship...

lisper 4y ago
This just occurred to me: > Perfect insulators do not exist Then it is not possible for any systems ever to be in thermal equilibrium before the heat death of the universe. So your definition of temperature is based on something that you yourself have said is physically impossible to achieve.
- krastanov 4y ago
  You are kinda right :D There is always a tension between rigor and practicality in theoretical physics (and frankly, in math -- just read how giants like Poincare felt about rigor or how Euler worked with infinite series in horrifically handwavy fashion). This level of hierarchical abstraction is pretty much the only tool we have though, and it seems it works better than whatever else we have tried. Axiomatic thermodynamics (the last couple of links in my previous post) does answer this particular problem though, it is just that no-one uses it.
  - lisper 4y ago
    This is not about rigor vs practicality, this is about logical coherence. You cannot base your definition of a physical quantity on a situation that is physically unachievable even in principle and expect to be taken seriously. > no-one uses it Gee, I wonder why. Here is how it's actually done: https://www.nist.gov/si-redefinition/kelvin-introduction https://www.nist.gov/si-redefinition/kelvin-introduction
    - krastanov 4y ago
      It really does not feel like you are taking this conversation up with intellectual honesty. For starters, rigor and logical coherence are the same thing. Second, the links I provided go into the rigor/logical coherence and already discuss the information from the link you shared in much more details. You can not at the same time complain about pedagogy (providing a handwavy explanation of entropy as the one that has better pedagogy) and rigor (providing a winding explanation that deals with all the intricacies but requires a lot of reading). Just get of your high horse and actually read through the things I shared. It is becoming silly to argue about entropy when you disregard half of the literature on the topic on a hunch. It is truly silly to share a pop-sci blurb from NIST in this situation. It certainly provides a good initial intuition, but it skips all the rigor and logical coherency you pretend to care about (and which, again, is discussed in what I shared).

lisper 4y ago

This just occurred to me: > Perfect insulators do not exist Then it is not possible for any systems ever to be in thermal equilibrium before the heat death of the universe. So your definition of temperature is based on something that you yourself have said is physically impossible to achieve.

krastanov 4y ago
You are kinda right :D There is always a tension between rigor and practicality in theoretical physics (and frankly, in math -- just read how giants like Poincare felt about rigor or how Euler worked with infinite series in horrifically handwavy fashion). This level of hierarchical abstraction is pretty much the only tool we have though, and it seems it works better than whatever else we have tried. Axiomatic thermodynamics (the last couple of links in my previous post) does answer this particular problem though, it is just that no-one uses it.
- lisper 4y ago
  This is not about rigor vs practicality, this is about logical coherence. You cannot base your definition of a physical quantity on a situation that is physically unachievable even in principle and expect to be taken seriously. > no-one uses it Gee, I wonder why. Here is how it's actually done: https://www.nist.gov/si-redefinition/kelvin-introduction https://www.nist.gov/si-redefinition/kelvin-introduction
  - krastanov 4y ago
    It really does not feel like you are taking this conversation up with intellectual honesty. For starters, rigor and logical coherence are the same thing. Second, the links I provided go into the rigor/logical coherence and already discuss the information from the link you shared in much more details. You can not at the same time complain about pedagogy (providing a handwavy explanation of entropy as the one that has better pedagogy) and rigor (providing a winding explanation that deals with all the intricacies but requires a lot of reading). Just get of your high horse and actually read through the things I shared. It is becoming silly to argue about entropy when you disregard half of the literature on the topic on a hunch. It is truly silly to share a pop-sci blurb from NIST in this situation. It certainly provides a good initial intuition, but it skips all the rigor and logical coherency you pretend to care about (and which, again, is discussed in what I shared).