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Regarding:
Some
teachers even try to smooth this over by introducing the "flow
of entropy" as a helpful concept!
This would not help any understanding of entropy. Fortunately, I have
not encountered this teaching technique.
When I wrote this last comment I meant that I had not encountered
teachers or professors making an appeal to the flow of entropy to help
explain the concept of entropy. I did not mean to suggest or imply that
textbooks didn't ever use the concept of entropy flow. However, thermo
books with an engineering slant tend to use entropy flow a lot more than
physics-oriented stat mech books though (in spite of Schroeder's cartoon).