Entropy is the logarithm of the total number of possible states of a system’s macroscopic distribution. In the demonstration below, the state of any particle is simply which side of the box it is on, left or right. Consider the simple situation in which there are two particles A and B, one on each side of the box. This system has two possible states that look the same if you don’t keep track of the individual particles: A on the left and B on the right, or B on the left and A on the right. Therefore, it has non-zero entropy ($\ln(2) = 0.69$). However, when both particles are on the left side, only one state is possible, resulting in an entropy of 0. The same is true when both particles are on the right side, which is its own macroscopic distribution. Use the controls in the top right to add more particles to the simulation and observe how the entropy changes depending on their distribution. Then, go to the controls and select “Maxwell’s Daemon”. What happens to the entropy as the particles all collect on one side?
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