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I recently read about Chaos Theory and was wondering if a chemical reaction results in or shows characteristics of chaos (I found a few examples of such reactions here)

Chaos theory concerns deterministic systems whose behavior can in principle be predicted. Chaotic systems are predictable for a while and then 'appear' to become random.

If the reaction becomes unpredictable towards the time of attainment of equilibrium we can't possibly determine how the reaction will proceed during the time frame so will the reaction attain a state of equilibrium and will it be at the time it should've without chaos being in the picture?

If the equilibrium shifts can we quantify by how much and how much more or less time will it take to attain it in general or we need to take specific reactions and analyze them?

Also after attaining equilibrium can the system again show Chaotic behaviour and if it does what can se say about the state of equilibrium?

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    $\begingroup$ Indeed, there is quite a bit of chaos in chemical reactions. I wonder, though, what's the point of your question. $\endgroup$ – Ivan Neretin Aug 24 at 19:51
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    $\begingroup$ @Mithoron your analogy isn't helping. I am simply asking whether the reaction will attain equilibrium at the time when it would've if there was no chaos or not? It's a binary question also if it doesn't then why and how can we find out the deviation at the point of time equilibrium and also when it does will it ever re-enter a chaotic state and when it does will the equilibrium shift? Sorry if my previous (deleted) comment was not friendly it was a mistake keeping the caps lock on $\endgroup$ – StackUpPhysics Aug 24 at 20:34
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    $\begingroup$ My comment did answer that: chaotic regime does somewhat alter time of completion of reaction and when it's complete, it's complete. $\endgroup$ – Mithoron Aug 24 at 22:10
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    $\begingroup$ What Mithoron says is based on chemical common sense. The very basics of thermodynamics and kinetics. If you want to quantify anything, you should be a lot more specific about the system. $\endgroup$ – Karl Aug 25 at 11:29
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    $\begingroup$ I think the point of chaotic (nonlinear) behavior is precisely that prediction becomes difficult and not amenable to standard linear methods. However you can probably bracket the expected response such as the time to equilibrium (provided the system is not continuously driven), as well as say something about the duration of intervals during which the system may behave "chaotically". You may want to consult a physics or math source for more details, or read more about the individual reactions you cite. $\endgroup$ – Buck Thorn Aug 25 at 13:05
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A homogeneous reaction mixture can hardly show macroscopical chaotic behaviour. Well known cyclic counterexamples exist, and practically any reaction which proceeds faster than diffusion or mechanical mixing can homogenise it again (e.g. any reaction that generates a lot of heat!) is liable to show some intermediate chaotic concentration gradients. Its usually hard to notice, and most reactions are perfectly reproducible, if you set them up in the same way (educt impurities!).

If your reaction vessel contains inflows of different chemical composition, then you easily get chaotic behaviour. Think about a tube reactor. I believe chemical engineers are spending a lot of their time trying to control and avoid chaos.

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  • $\begingroup$ Thanks for the info but this doesn't exactly answer my question $\endgroup$ – StackUpPhysics Aug 25 at 11:06
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    $\begingroup$ @StackUpPhysics Then I also do not understand your question. $\endgroup$ – Karl Aug 25 at 11:25
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    $\begingroup$ @StackUpPhysics Are you seriously asking wether a system can stay chaotic when it has reached thermodynamic equillibrium? And of course a chaotic system will take a different amount of time to reach equillibrium than a reaction that just progresses straigthforward. It is a different system, after all! $\endgroup$ – Karl Aug 25 at 15:19
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    $\begingroup$ One hint, perhaps that is behind your misunderstanding: Chaos is by no means a state of maximal entropy. Chaotic systems usually show selfsimilarity! Thermodynamic equillibrium IS the point of maximal entropy, and there is no way out of it. $\endgroup$ – Karl Aug 25 at 15:29
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    $\begingroup$ Why do you think it is called equillibrium? When have you ever seen that something that was in motion and has come to rest suddenly starts rolling uphill again? $\endgroup$ – Karl Aug 26 at 6:02
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What I think: A macroscopic chaotic system is a system whose "components" influence each other, and the macroscopic outcome depends on the status of the components. This happens for the two-arms pendulum, for air particles in cigarette smoke, and for particles in wind. Each microscopic variation can be propagated between particles, and the final status of the system can vary a lot, as varies the status of the particles (eg: temperature, position).

Typical chemical reactions, at the typical macroscopic level have different features: they show "average" properties of the microscopic systems of which they are made (that's the base of statistical thermodynamics, and of Boltzmann's law).

Anyway, if we look closer, we might find chaos, after all: fluctuations of thermodynamic properties arise from the microscopic cause of macroscopic properties (for example, if the temperature of a liquid was mesured with extreme precision every picosecond, it would show variations arising from the way the particles hit the sensor). The variations arise from complex interactions between the microscopic components, and they are non-predictable. That is chaos, albeit not as "macroscopic" as the behavior of cigarette smoke or of the double pendulum.

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  • $\begingroup$ Chaos means that you have variations at least on a mesoscopic lenghtscale, and it absolutely needs an energy source, unless you have a completely lossless system. Its not to be confused with high entropy. The surface shape of a cloud is highly structured, selfsimilar and chaotic, fog (or the inside of the cloud) isn't. en.wikipedia.org/wiki/Belousov%E2%80%93Zhabotinsky_reaction#/… $\endgroup$ – Karl Aug 27 at 20:35

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