Abstract
In statistical mechanics, the generally called Stirling approximation is actually an approximation of Stirlingâs formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account. The use of the Stirlingâs exact formula forces us to reintroduce them into the already proposed solutions of well-know puzzles such as the extensivity paradox or the Gibbsâ paradox of joining two volumes of identical gas. This amendment clearly results in a gain in consistency and rigor of these solutions.
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