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Slow down and think, folks! Energy is not a thing; it is not real.
-> There is no such thing as "pure energy". <-
[energy nonreality] is a fundamental physical principle, as you will...
see by an example of its application.
One invokes the arbitrary nature of the
zero of energy and the result (the Boltzmann factor) drops out
entirely naturally. There is no way I know to derive it otherwise.