I have to say that my mind was blown by a book this weekend.

[Bernardo de La Paz]

7. Hmm, was looking for background but got lost immediately

https://en.wikipedia.org/wiki/Boltzmann's_entropy_formula

I'm having trouble with the concept of microstates. If a microstate is a designation of the position and momentum of a particle, are there not as many microstates as particles? Since each particle's position and momentum are real numbers, different from the other particles' real numbers?

In statistical mechanics, Boltzmann's equation (also known as the Boltzmann–Planck equation) is a probability equation relating the entropy S {displaystyle S} S, also written as S B {displaystyle S_{mathrm {B} }} {displaystyle S_{mathrm {B} }}, of an ideal gas to the multiplicity (commonly denoted as ? {displaystyle Omega } Omega or W {displaystyle W} W), the number of real microstates corresponding to the gas's macrostate:

S = k ln (W)

Or is W (or Omega) somehow a probability distribution?

Or does it mean a container of gas has more entropy if it contains more gas?

https://en.wikipedia.org/wiki/Microstate_%28statistical_mechanics%29

Note: not anyone's problem except my own; just musing out loud.