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blue2script

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I have a question arising from my course in statistical physics: Describing microcanonical, canonical and grandcanonical ensemble you take three variables (like E,V,N for microncanonical) and get the "rest" from derivatives of the free energies. Is there a deeper meaning why there are only three variables to be fixed and not four or five?

Another question: Is there any deeper meaning that all free energies transform into each other by Legendre transformations? There should be. Any references on these topics that could be helpful?

Thanks for all answers and help!

Blue2script