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My AP biology textbook, (the 10th edition of Campbell Biology) states entropy as being the disorder or randomness of the atoms involved in any matter, but Khan Academy says that this example isn't quite right, and is too simplistic of a way of explaining the concept. And the TedED video I watched goes on talking about quanta and stuff ...

The online definition I was able to find of entropy on Wikipedia states the "The entropy of an object is a measure of the amount of energy which is unavailable to do work. Entropy is also a measure of the number of possible arrangements the atoms in a system can have. "

I'm confused how it's both at the same time and how they're related. And how does this even relate back to Biology again???

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  • $\begingroup$ check this video youtu.be/8N1BxHgsoOw?t=63 and this: youtu.be/tFmJ4uVNX44?t=36 and youtu.be/Svvr5uF_FZ8?t=187 and some other vids :D youtu.be/9PGNeFmEFa8?t=1523 and youtube.com/watch?v=Ntdqft89_e4 $\endgroup$
    – bandybabboon
    Dec 6, 2019 at 5:53
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    $\begingroup$ If you want the concept of entropy explained, this is not on-topic for this site. In the general sense this is physics, but as it relates to chemical reactions, would be suitable for our sister site SE Chemistry. I would also suggest you read the account in Berg's Biochemistry. There are specific areas of biology and biological chemistry — not metabolic reactions, which are just chemistry — that raise particular problems in relation to the second law, but it does not seem that you are asking about these and that your question is off-topic. $\endgroup$
    – David
    Dec 6, 2019 at 14:30
  • $\begingroup$ It seems to me that the question you have that it relevant to this site, is not the definition of entropy, but why it appears in biology book in a section on metabolism. I do not own a copy of Campbell so cannot check the section, but I can explain why it appears in the section of Berg et al. that I quoted in my other comment. It may be this is the reason it is mentioned in the less chemical Cambell. If you wish an explanation, could you please read through the section, accepting his definition of entropy, and tell us where it leads. Does it lead to the Gibbs Free Energy of coupled reactions? $\endgroup$
    – David
    Dec 7, 2019 at 13:18

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2nd law of thermodynamics states that the overall entropy of the universe cannot decrease at any time. This can also be stated as the fact that the universe naturally falls towards the lowest energy state, or equilibrium. This becomes important in metabolic reactions. Reactions which seem to increase the state of energy, or perhaps the 'order' of the universe, have done so at the expense of another part of the universe, usually through the conversion of energy from molecules such as ATP or NADPH.

Think of the ATP Synthase on the cell membrane. It is creating ATP (Adenine tri-phosphate) molecules from ADP (adenine di-phosphate) and a phosphate group. This too seems like a system changing molecules from a low energy state to a high energy state. It is, but it can only do so by the natural flow of H+ ions which have accumulated on one side of the cell membrane and naturally flow from their high concentration to their low concentration on the other side. So while the ATP synthase molecule is making higher energy molecules (decreasing entropy) it is doing so as H+ naturally flows towards equilibrium, which increases the overall entropy in the universe.

In essence: things are always going towards a low energy state, i.e. equilibrium, i.e. maximum entropy. If any system goes against this, it does so via an outside energy source which has increased the entropy of the universe somewhere else.

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    $\begingroup$ +1 for describing entropy without using the word "random" and avoiding usage of "disorder". $\endgroup$
    – user40950
    Dec 6, 2019 at 14:14
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    $\begingroup$ I don't understand why you have to use the complex ATP synthase as an example. Surely any metabolic reaction would do, or indeed any chemical reaction as enzymic catalysis has no effect on the energetics. $\endgroup$
    – David
    Dec 6, 2019 at 14:36
  • $\begingroup$ (Pt. 1) I think I have a better idea of entropy now, my definition and example in my notes are as follows: Entropy is the measure of thermal energy in a system, thermal energy referring to the concentration of energy in bonds between molecules, this concentration naturally falls twords reaching equalibrium or the equal dispersion of energy between all bonds, when something is closer to equalibrium it cannot be used for work and carries less information. $\endgroup$
    – Clay A.
    Dec 7, 2019 at 22:35
  • $\begingroup$ (Pt. 2) For example, water is free flowing with energy bouncing between its molecules and is more stable then say, ice, which is structured and carries the information of it's structure, has fewer degrees of freedom for it's energy to flow, and want to melt into water to become more stable (spontaneously) It takes work to freeze water into ice (it's most natural ordered state) but work cannot be applied to water to make it anything more than plasma. $\endgroup$
    – Clay A.
    Dec 7, 2019 at 22:43
  • $\begingroup$ (Pt. 3) This is why it requires work (ATP) to create complex biological molecules, however life still increases the overall entropy of the universe because of the citric cycle and being "wirlpools" of moving matter becoming simpler forums $\endgroup$
    – Clay A.
    Dec 7, 2019 at 22:45
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As tax money is no longer available for you payments, entropy is the tax of nature in that it is the energy taken (leaked) from your system, be it supplied or produced, that is no longer available for work.

You have to pay the tax (entropy) for every activity involving energy (money) other wise your activity will not be possible. If your activity involves lots of properties (number of particles or large size of the system, therefore higher degrees of freedom) you have to pay a higher tax ( termed entropic penalty). If your activity involves fancy properties (not so large number of particles but a highly flexible molecules in themselves, hence again higher degrees of freedom) again you have to pay a higher tax.

Carnot realized the concept of entropy when he was trying to design a perpetual motor.

He concluded that as long as the motor is made of material that consists of particles there will be leakage of some energy to the particles by means frictional dissipation and you cannot convince the particles not to do so. You can only minimize this leakage by choosing a system that has the least possible degrees of freedom. This applies to literally every thing (every energy-involving activity or process) from biochemical reactions to electromagnetic radiation too (their particles are termed photons), and so it is a universal principle.

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  • $\begingroup$ I am afraid this answer does not relate the concept of entropy to metabolism or even biology in general, so does not address the part of the question that is on-topic for this site. $\endgroup$
    – David
    Dec 6, 2019 at 14:21
  • $\begingroup$ Is it nearer to the topic now ? @David $\endgroup$
    – M.ghorab
    Dec 6, 2019 at 15:04
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    $\begingroup$ By inserting “biochemical” in front of “reactions”? $\endgroup$
    – David
    Dec 6, 2019 at 19:19
  • $\begingroup$ Maybe, however, do you have any technical criticism for the answer? $\endgroup$
    – M.ghorab
    Dec 7, 2019 at 10:55
  • $\begingroup$ My main concern with this question and answers to it is the relation to biology in general and metabolism in particular, as laid out in my detailed comment to the poster. This is so things remain appropriate for SE Biology. I will comment on answers if I think they are factually incorrect, especially if they have been upvoted, but otherwise I would not wish to discourage new contributors to the site. As for "technical criticism": you present a "tax" analogy that you think may help the poster. Only the poster can say whether or not it does so, although I personally would doubt it. $\endgroup$
    – David
    Dec 7, 2019 at 12:54

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