From https://johncarlosbaez.wordpress.com/2021/08/05/information-geometry-part-18/ a discussion of entropy analogies using probability

> "Similarly, a probability distribution ‘wants’ to flatten out, to maximize entropy, and p_i says how eager it is to increase the probability q_i in order to do this."

> ![](https://pbs.twimg.com/media/E8DUfIQUYAIOuCQ.jpg)

The lower right is essentially the power spectrum of the upper right, see this discussion:

https://johncarlosbaez.wordpress.com/2021/08/08/information-geometry-part-19/#comment-171330

> "Similarly, a probability distribution ‘wants’ to flatten out, to maximize entropy, and p_i says how eager it is to increase the probability q_i in order to do this."

> ![](https://pbs.twimg.com/media/E8DUfIQUYAIOuCQ.jpg)

The lower right is essentially the power spectrum of the upper right, see this discussion:

https://johncarlosbaez.wordpress.com/2021/08/08/information-geometry-part-19/#comment-171330