1. Are the low multiplicity macrostates prohibited?
If you are asking are they impossible the answer is no.
2. Are the high multiplicity macrostates certain?
They are more likely but they are not 100%.
3. Are low entropy states prohibited?
Not impossible just unlikely.
4. Are high entropy states certain?
Not just certain, just more likely.
5. If you started out with the coins in a lower entropy state (say with 2 heads out of 10 coins) is it
possible that you might, if you tossed the coins again, arrive at a lower entropy state (say with 0 or 1
heads)?
It is possible to get a lower entropy state but it is unlikely. You are more likely to get a higher entropy
state
6. Is this likely to happen?
You are more likely to get a higher entropy state over a low entropy state. If you flipped those 10 coins
you have a higher chance of getting 5 heads out of 10 rather than 1 or 0 heads or even 9 or 10 heads.
7. Which of the following would you agree with:
A system can never go from higher entropy to lower entropy.
Disagree. It’s possible to go from a higher entropy to a lower entropy but it is a little more unlikely the
more extreme it gets.
A system will always go in the direction of higher entropy.
Not always but it is the most likely scenario.
A system will usually go from a lower entropy state to a higher entropy state.
Not always but a higher entropy state has a better probability of happening
8. Would you agree so far with this statement of the Second Law of Thermodynamics:
In a closed system (in this case one where we don’t reach in and flip coins over after they come to rest
following a toss) entropy must always increase.
Yes I agree with this statement.
Explain. If you disagree, what would you say instead?
Basically if you have a bunch of various outcomes possible, it is more likely to go towards a higher
entropy state.
9. What happens to the probability of the lowest entropy states as the number of coins increases?
The more options there are the less likely the lower entropy states are likely to happen.
10. With a closed system with a lot of coins (or atoms or molecules) would you agree with stating the
Second Law of Thermodynamics this way:
Entropy in such a system is not certain to increase with time but very, very likely to do so.
Yes I would agree with this statement.
11. Suppose you saw a picture of a set of 10 coins with only 1 of the coins heads up and also a picture
of the same set of 10 coins with 4 of the coins heads up, which one would you say occurred first?
I would say that the 4 occurred first. The higher the entropy state the more likely it is to happen
12. Is it fair to say that entropy shows an arrow of time?
Yes. As time progresses the entropy is more likely to slow down.
13. Does the arrow become more or less distinct with an increase in the number of coins (or atoms or
molecules)?
Looking at the graphs I would say that in the beginning it would be very distinct, but then becomes less
so as time goes on.
14. Is there a connection between probability, entropy, the Second Law of Thermodynamics and time?
I don’t know the Second Law of Thermodynamics, but the connection between the others is a
predisposition towards high entropy probability at the beginning but as time progresses entropy lowers
and then stops.