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I have previously heard that some scientists are interested in trying to reformulate statistical mechanics in different ways to try and create new ways to solve novel problems.

This got me wondering, what are the fundamental "components" that you would need to re-derive to have a fully (or mostly) equivalent formulation of statistical mechanics? In essence, if you were to create a list of concepts, like the ergodic principle, partition function, quantum distributions, law of entropy, etc., what fundamental tools would you need to have in order to be able to derive many of the useful results of statistical mechanics, (for example the equipartition of energy, fermi/bose energies, the classical limit for gases)?

For example, we need the idea of discrete states, self-interference, the pauli exclusion principle, and some kind of energy relationship (like the hamiltonian) before we would be able to make ladder operators for the QM SHO, or derive it's energy levels.

To clarify, let's just say we were interested in constructing a tree graph of statistical mechanics in a way that was analogous to this outline of thermodynamics enter image description here

What would be the concepts the first "step" down on the tree for Statistical Mechanics?

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  • $\begingroup$ possible duplicate: physics.stackexchange.com/questions/19849/… $\endgroup$ – Martin Jan 29 '15 at 14:04
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    $\begingroup$ The use of the word axiom isn't intended to be rigorous. I'm not asking for some kind of mathematical abstraction of statistical mechanics. I'm just asking: What are the portions of statistical mechanics that we use to derive the rest of it? $\endgroup$ – Skyler Jan 29 '15 at 19:08
  • $\begingroup$ How abbout this: A human physicist and an alien physicist go to a bar, and decide to talk about statistical mechanics. What do they have to agree on, even if both species developed a different systems of math and their two models of statistical mechanics look different (superficially). $\endgroup$ – Skyler Jan 29 '15 at 19:27