The Second Law of Thermodynamics: Heat Flow, Entropy, and Microstates

What the heck is entropy?! You've heard a dozen different explanations. Disorder, microstates, Carnot engines... so many different wordings and interpretations! Really, they are all related, so let's go through a few different formulations of the second law and ways of interpreting it. It's hard to understand, but who doesn't like a challenge?

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