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Callen (postulate II) postulates the existence of the entropy as the quantity to be minimized (or maximized, he will talk about that later) to achieve equilibrium. Why does he postulate the entropy rather than sticking with energy? It seems like he's making a leap that he doesn't justify, even though I know from the Second Law (which he dispenses with in his presentation) that the entropy exists.

Qmechanic
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In classic thermodynamics, the existence of entropy, and that is is maximum at equilibrium, is a postulate. An axiom. This means that it is not "justified". There is no explanation of why. As you say, it is leap. Fortunately, the postulates are the only leaps. Everything else in the theory can be mathematically proven from those postulates.

The theory, with this postulate, ends up correctly predicting multiple phenomena. This is how postulates are ultimately "justified".

Note that there is another theory, Statistical Mechanics, were entropy is not a postulate, and it can be deduced from SM's own postulates. It provides a satisfying explanation of from where entropy comes.

Juan Perez
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