Link between quantummechanical probabilistics and entropy

[entropy1]

I am an amateur on physics. Lately I have been thinking about this: Is there a link between quantummechanical probabilistics and entropy?

I can put it into words like this: "Entropy: The greatest possible chance that outcomes even out (are as similar as possible)."

For instance: The chance that an off-axis polarized photon passes the filter. Sometimes it does, sometimes it doesn't, but take a large number of measurements, and the correlation between angle and probable pass-through are inexcapable. I don't know very much about thermodynamics, but I figured that pressure in a closed box with gas also 'evens out' due to entropy (the particles becomes evenly spread), so that the probability a particle has a specific momentum becomes as great as possible. Similar, the probability a photon passes the filter is directly proportional to the angle of the filter, so the proportion of particles that pass to those blocked is 'evenly spread'... (grosso modo, each photon 'behaves' similar, or at least, becomes more statistically probable to do so...)

Does this make the tinyest bit sense?

I hope you can forgive me my poor english.

 

[Vanadium 50]

First, I don't see why we need a different definition of entropy than what is in the textbooks.

Second, there is no tendency for outcomes to "even out". Every trial is independent of previois trials.

 

[entropy1]

Every trial is independent of previois trials.

First, I don't see why we need a different definition of entropy than what is in the textbooks.

I was thinking there might be a correlation between outcomes of different measurements, like in quantumentanglement, a way of nature to compensate information that occurs in one part in the universe, in the other part of it, so that the independent appearance of outcomes is just an illusion. I am not sure if I state this correctly: Of all the states of a given system, the one with the highest entropy is the most likely one.

I feel my knowledge falls short here I will try to catch up a bit.