I've written a few pieces on the entropy physicists talk about as well as the sort-of-not-really related entropy of computer science. Popular culture calls it disorder, but that's misleading.
Derek Muller posted a good discussion that doesn't assume any background but gets much of the core right (that's a difficult balance!) He spends a lot of time on these videos and it shows.
An added note. The twenty photons out for every photon in is an average, but is fairly accurate. Your body emits photons too.. in fact they're a bit more energetic than what the Earth gives off, but not quite enough to say nineteen photons out for every one in..
Entropy became formalized in statistical mechanics. The introductory paragraph of the textbook States of Matter by David Goldstein is one of my favorites.
INTRODUCTION: THERMODYNAMICS AND STATISTICAL
MECHANICS OF THE PERFECT GAS
Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics.
Perhaps it will be wise to approach the subject cautiously.
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