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- In the scenarios of a coin flip and the motion of gas molecules, what is really at play: true randomness or chaos?

Note: This question involves both classical and quantum physics, so I didn't know where to put it.

I'll start with the coin flip:

People often compare electron spins to a coin flip, citing that coin flips are random. I am wondering if that is a true analogy, or just another faulty analogy between classical and quantum physics. My thinking is that while coin flips appear random, if you are given the the torque on the coin, the trajectory of the wind, and the initial state of the coin (including its position and whatnot), one could determine with certainty the result of the flip. This would be like a chaotic (local) hidden variable behind the result of the coin flip, which is forbidden in the case of electron spins. Given this, are coin flips purely random (like a quantum system), or do they just appear random due to underlying classical physics?

Now, with the gas:

Though there is an element of quantum mechanics at play here, I'm wondering if the "random motion" of a gas assumed in the kinetic theory is truly randomness. Say you zero in on each molecule and measure its position to an uncertainty of one micrometer, and then measure its momentum to the lowest uncertainty allowed. Though these may be large uncertainties for the size of the molecule, in terms of a 20L container, we know what that molecule is doing pretty well. Is the randomness here a result of true quantum randomness, or is it just due to the number of molecules that are all sensitive to initial conditions? That is, if I had to an allowed level of uncertainty the positions and momenta of every molecule, could I predict how the molecules would distribute over time?

Also, I'm not positive if I am using the term chaos correctly, but I think I am. Please correct me if I'm wrong.

Thank you in advance!

I'll start with the coin flip:

People often compare electron spins to a coin flip, citing that coin flips are random. I am wondering if that is a true analogy, or just another faulty analogy between classical and quantum physics. My thinking is that while coin flips appear random, if you are given the the torque on the coin, the trajectory of the wind, and the initial state of the coin (including its position and whatnot), one could determine with certainty the result of the flip. This would be like a chaotic (local) hidden variable behind the result of the coin flip, which is forbidden in the case of electron spins. Given this, are coin flips purely random (like a quantum system), or do they just appear random due to underlying classical physics?

Now, with the gas:

Though there is an element of quantum mechanics at play here, I'm wondering if the "random motion" of a gas assumed in the kinetic theory is truly randomness. Say you zero in on each molecule and measure its position to an uncertainty of one micrometer, and then measure its momentum to the lowest uncertainty allowed. Though these may be large uncertainties for the size of the molecule, in terms of a 20L container, we know what that molecule is doing pretty well. Is the randomness here a result of true quantum randomness, or is it just due to the number of molecules that are all sensitive to initial conditions? That is, if I had to an allowed level of uncertainty the positions and momenta of every molecule, could I predict how the molecules would distribute over time?

Also, I'm not positive if I am using the term chaos correctly, but I think I am. Please correct me if I'm wrong.

Thank you in advance!