Question

How does entropy relate to chaos theory?

Answer 1

Hint: The term chaos means complete disorder and confusion. Entropy can be elaborated as the randomness of particles in a system. One can relate the term chaos with the concept of entropy and can give some examples to make the relation between the two terms.

Complete step by step answer:
1) First of all, after knowing the two terms we can relate the term entropy is related to chaos theory as it is a general measure of “Disorder”. The term entropy can be elaborated in form of a formula as below,
$\mathrm{\Delta }S={\displaystyle \frac{\mathrm{\Delta }{Q}_{rev}}{T}}$
Where $\mathrm{\Delta }S$ is entropy
$\mathrm{\Delta }{Q}_{rev}$ is heat change in a reversible process
T is temperature
2) Now, the heat flow is not a state function instead it’s a path function. Actually, the basic concept of the chaos theory that relates to entropy is the idea that the system leans towards “Disorder”.
3) The universe is a chaotic system, if we drop a bunch of non-sticky balls on the ground, we can’t guarantee that they will stay together and fall on the same spot every time and stay in place after falling. This process is very much entropically favorable for them to separate from each other.
4) We cannot predict exactly how they will fall, even if we make them stick the ball system will be decreased in entropy simply from falling and becoming separate from the human system.
Therefore, we can say that entropy relates to chaos theory.

Note:
Now it is proven that we can determine the initial and final state without worrying about the path to get there. This is confirmed because in the chaotic system we can’t predict the final state. Entropy is a state function which means it doesn’t depend on the path of reaction.