What Is Entropy?

I don’t see Sean Carroll’s musings mentioned yet, so repeating my previous comment:

Entropy got a lot more exciting to me after hearing Sean Carroll talk about it. He has a foundational/philosophical bent and likes to point out that there are competing definitions of entropy set on different philosophical foundations, one of them seemingly observer dependent: - https://youtu.be/x9COqqqsFtc?si=cQkfV5IpLC039Cl5 - https://youtu.be/XJ14ZO-e9NY?si=xi8idD5JmQbT5zxN

Leonard Susskind has lots of great talks and books about quantum information and calculating the entropy of black holes which led to a lot of wild new hypotheses.

Stephen Wolfram gave a long talk about the history of the concept of entropy which was pretty good: https://www.youtube.com/live/ocOHxPs1LQ0?si=zvQNsj_FEGbTX2R3

Half a year after that talk Wolfram appeared on a popular podcast [1] to discuss his book on the Second Law of Thermodynamics [2]. That discussion contained the best one-sentence description of entropy I've ever heard:

> Entropy is the logarithm of the number of states that are consistent with what you know about a system.

[1]: Mystery of Entropy FINALLY Solved After 50 Years? (Stephen Wolfram) - Machine Learning Street Talk Podcast - https://www.youtube.com/watch?v=dkpDjd2nHgo

[2]: The Second Law: Resolving the Mystery of the Second Law of Thermodynamics - https://www.amazon.com/Second-Law-Resolving-Mystery-Thermody...

By that definition, the entropy of a game of chess decreases with time because as the game moves on there are less possible legal states. Did I get that right?