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Well you're giving the statistical mechanics explanation (or information theory), which some thermodynamicists don't appreciate so much, but... I totally agree.

• lisper 4y ago
  > some thermodynamicists don't appreciate so much Why?
  • krastanov 4y ago
    You do not need statistical physics to define entropy. In fact, entropy as a concept was introduced long before statistical physics was a thing. Being able to do thermodynamics without invoking anything related to statistical physics is very valuable tool in mathematical physics, as it leads to definitions and proofs that rely on way fewer assumptions. People should not claim they understand entropy if they understand only the statistical physics way of introducing it. The deep value of the concept of entropy comes from understanding how the two completely unrelated definitions (in thermodynamics and in statistical physics) are equivalent. Edit to add: In statistical physics you rely on the idea of equivalent microstates. In thermodynamics you do not introduce anything about the microscopic structure of the system under study (an extremely valuable way to generalize your results to cases not covered by typical stat physics assumptions), rather you introduce the zeroth law of thermodynamics as an axiom.
    • lisper 4y ago
      > entropy as a concept was introduced long before statistical physics was a thing That's true, but the historical development doesn't always make for the best pedagogy. Quantum mechanics, to take my favorite example, is vastly simpler than it is commonly made out to be [1]. It just took about 80 years for this to be understood. The development of thermodynamics followed a similar path because thermodynamics predated the widespread acceptance of the atomic theory. Indeed, statistical mechanics played a major role in getting the atomic theory accepted. But it does not follow that the thermodynamic treatment is superior in any way. I challenge you to explain to me what entropy actually is in fewer words than I used without reference to atoms or microstates. I'll bet you can't even explain what "temperature" is under those constraints, and that is much simpler. --- [1] See https://en.wikipedia.org/wiki/Quantum_Computing_Since_Democritus https://en.wikipedia.org/wiki/Quantum_Computing_Since_Democr... chapter 9
      • krastanov 4y ago
        You are right about pedagogy. But "understanding" requires much more than giving one simple definition without discussing the consequences of the definition. Your (statistical) definition of entropy is perfectly reasonable and fairly intuitive and it should be taught first (as you alluded twice and as it is relatively common these days). But "understanding" entropy involves understanding multiple facets of it and why it is useful, not just knowing the easier definitions. Hence, it seem unreasonable to claim "understanding" entropy without having familiarity with the independent thermodynamic definition of entropy and *why are they equivalent*. That would be like saying one understands programming language theory while being familiar only with object oriented programming. Using atoms and microstates to explain entropy makes the explanation shorter but it also makes it *more* complex because it now depends on the definition of *atoms and microstates*. The thermodynamics explanation of entropy does not actually require more words, but crucially, it requires fewer concepts (heat, useful work, and heat transfer). Concerning the development of thermodynamics: defining entropy *without* statistical physics requires *fewer* assumptions about the physical system. Statistical physics did not make thermodynamics simpler, nor is it necessary to explain thermodynamics. To your example about quantum mechanics: this is different because statistical physics is not some better more-fundamental explanation of thermodynamics. The two are separate sets of axioms with equivalent explanatory power. Concerning the definition of temperature: are you aware that there is an implicit assumption about temperature scales when defined in the statistical physics way? That is much more explicit in the thermodynamic treatment. And it is why I brought up the zeroth law of thermodynamics: it is where temperature is defined. If you think temperature is easier to define in the statistical physics setting, you are simply hiding a ton of assumptions under the rug, which is not a very good way to build a mathematical theory. I am curious what do you claim is a simple statistical explanation of temperature? If it is something about average energy, that is a *wrong* explanation of temperature, valid in only a few special circumstances. As to actually giving you the thermodynamic definition of temperature: The joke is that it is whatever the thermometer says it is. The rigorous version of that joke is: According to the zeroth law of thermodynamics, if bodies A and B are in thermal equilibrium (no heat transfer) and bodies B and C are in thermal equilibrium, then A and C are also in thermal equilibrium. Use this equivalence property to tag all bodies that belong to the same equivalence class. This tag is your measure of temperature. It is an arbitrary (ordered) scale. If you want to, you can then use the second law of thermodynamics to pick a neater canonical scale. Finally, the definition of entropy: enumerate the (macroscopic) variables describing your system and draw them as a coordinate system; compute the value of ΔQ/T as you travel through some path in that coordinate system; the second law of thermodynamics says that value is zero on a closed path, thus we have a potential function; name that potential function entropy. Mathematically, in many aspects that is both a simpler and a more powerful definition. One could hardly claim to understand entropy if they do not understand the enormity of the previous paragraph and its relationship to the independent statistical definition. TLDR: "Understanding" entropy is about understanding why these vastly different definitions (thermodynamic and statistical) are equivalent, not about being able to recite one or the other. Especially given that statistical physics is not more fundamental than thermodynamics (unlike special relativity which is indeed more fundamental than Newtonian gravity)