After having completed 2 years of a Bachelor's degree, the only definition of entropy I know is [tex]\Delta S = \int_1^2 \frac{dQ}{T}[/tex]. I realize it's the change of entropy rather than the entropy of a system.(adsbygoogle = window.adsbygoogle || []).push({});

My question is "Is this the only definition of entropy"? I've seen in wikipedia and Fundamentals of Physics (Resnick-Halliday) the definition [tex]S=k \ln \Omega[/tex] but I never learned it nor do I understand what it means.

In the case of 2 isolated iron spheres in the Universe that are separated by a distance d. When they get closer and closer to each other, does the entropy of the system (the 2 spheres) increases? With the definition I have from entropy, heat is not involved so the formula is not useful.

Because I realize that the 2 spheres will only get closer and closer and if I could record a film of the motion, I'd realize instantly if the film passes reversely or not.

Assuming that yes, entropy increases in the example... I have another question:

Do you buy that it's IMPOSSIBLE for a sphere not to get closer to the other?

It's different than in the case of having a gas confined into a 1 m^3 cube we want to know whether the film passes reversely or not. Because there is a small probability that say 10^24 particles are confined into 10 cm^3 rather than in 1m^3 which is the volume of the container. Hence looking at the film, although I could almost always be right in telling the direction of the film, I could still be wrong (ok, I realize this won't happen within a very large time, even much greater than the current age of the Universe but I consider this as a possibility-improbability and not as an impossibility).

I wrote the last paragraph to show a distinction between what I consider impossible and what I consider improbable but possible. I would like to know if it is possible but improbable that the 2 spheres reduce their acceleration even for a very short time when they're getting closer to each other. I believe it's impossible and would violate Newton's laws (I'm pretty sure that it would also violate Relativity ones).

Thanks for all.

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# Entropy uncommon question(s)

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