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Okay, I'd like to preface this by saying I have done a lot of research on the idea of entropy, and nothing has clicked. Chaos doesn't have any mathematical value, and frankly, its entirely too vague. I understand that energy will always seek to dissipate and become uniform (through simple understanding of momentum), but what exactly is entropy saying? What was it that Carnot saw that didn't add up? or an experiment that he performed that wasn't what common sense would dictate?

Please refrain from describing the Boltzmann constant, etc that has been a more recent development. I'm trying to understand the origin to such a chaotic idea.

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  • $\begingroup$ Firstly, entropy is loosely associated with chaos; but it is not what entropy actually is. Also, in thermodynamics, it is not entropy but rather change in entropy that is explicitly analysed. $\endgroup$
    – user36790
    Commented Dec 9, 2016 at 4:27
  • $\begingroup$ This question may be more at home on History of Science SE. The short version is that the macroscopic description of entropy was developed long before any microscopic picture. This macroscopic picture was developed to answer questions like "why does heat flow from hot things to cold things but not the reverse" and "How can I make a more efficient steam engine". The microscopic picture was developed decades later to answer question like "what is this entropy that keeps springing up anyway?" $\endgroup$
    – By Symmetry
    Commented Dec 9, 2016 at 4:34
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    $\begingroup$ Entropy was first conceived by Rudolf Clausius not by Sadi Carnot. $\endgroup$
    – freecharly
    Commented Dec 9, 2016 at 5:09
  • $\begingroup$ I thought carnot, while not specifically calling it entropy, witnessed losses and is a precursor to Clausius' entropy? $\endgroup$
    – J. LeMoine
    Commented Dec 9, 2016 at 5:36

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I find it exceedingly hard to parse what you are trying to say. What in all the world do you mean by "chaos doesn't have any mathematical value"? Why do you think the mathematical concept of chaos is "entirely too vague"? You do understand that this concept does indeed have a precise definition in the theory of differential equations, or do you not? Finally, what in all the world do you think does any of this have to do with entropy?

Now, as far as entropy is concerned, what is it you are asking? You bring up Carnot in this question for reasons that are again somewhat mysterious, given that Carnot had only a very vague notion of the concept of entropy, and that it was in fact Rudolf Clausius who gave the first formal definition. There's a fairly good Wikipedia article on the subject which you may want to consult. That might turn out to be a better use of your time than trying to snow us with a bit of half-knowledge here and there...

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  • $\begingroup$ Chaos has no meaning. Its meaning is the composition of other meanings, therefore it is just a blanket statement used to describe many different phenomena. We describe what we do not know or cannot predict YET as chaos. What do I think it has to do with entropy? That would be part of the question I posed originally. I have absolutely no idea why the change in entropy is always described by your favorite term, chaos. I'm glad you noticed that Carnot had a vague notion of entropy, so if you know that much, answer me the original question - What did he know, and why did he know it? It's simple. $\endgroup$
    – J. LeMoine
    Commented Dec 9, 2016 at 7:39
  • $\begingroup$ Also, the linked article is the exact reason I posted the original question. You can see under Classic Thermodynamic Views that Carnot did in fact realize something was not right. This is what is vague to me and what I want to understand. I await your next comment with hopes that you bring something more to the table than a patronizing elitist attitude. $\endgroup$
    – J. LeMoine
    Commented Dec 9, 2016 at 7:46
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    $\begingroup$ "Chaos has no meaning": No. As I have tried to explain to you, the term "chaos" has a precise meaning in mathematics, and in physics. The fact that you are clearly ignorant of its meaning is of no epistemological relevance. And, no, change in entropy is rarely, if ever, linked to the concept of chaos, simply because the two have nothing to do with each other. Finally, I am sorry to say that I am quite unfamiliar with the complete contents of Carnot's consciousness at any point in time, so I am unable to answer a question as broad as yours. $\endgroup$
    – Pirx
    Commented Dec 9, 2016 at 12:18
  • $\begingroup$ If indeed you want to learn more about the history of the concept of entropy in classical thermodynamics, you should start with Clausius. These ideas are well described in the article I linked to. If you have questions regarding its content specifically as it pertains to the physics of entropy and would consequently like to rephrase your original question in a way that makes sense, we may be able to help. However, as someone else remarked above, if your focus is on the history of science aspect of this, then there's a more appropriate forum you should consult. $\endgroup$
    – Pirx
    Commented Dec 9, 2016 at 12:22
  • $\begingroup$ If I have an ignorance in the usefulness of describing something as chaotic, you have the ignorance in that entropy and chaos, while possibly having no inherent link, ARE described together in many textbooks and by many professors. I have no problem conceding that they may not linked, but to say that it isn't a common descriptor is ignorant. With that said, I wish you could have saved yourself and I some time. As you said, you don't know Carnot's thought process, which is exactly what I am after and was hoping someone here could shed some light on. $\endgroup$
    – J. LeMoine
    Commented Dec 10, 2016 at 8:38

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