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As I understand it, Noether's theorem is an important result that allows us to show when certain kinds of conservations arise. Is energy conservation in thermodynamics a result of Noether's theorem? If not, where does it come from? Or is it just an accepted axiom?

Qmechanic
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Stan Shunpike
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    Energy conservation in thermodynamics is expressed by the first law, which declares heat to be a form of (internal) energy that obeys energy conservation. From a statistical mechanics point of view this is a trivial consequence of energy conservation on the microscopic level. On some level the beauty of thermodynamics lies in the very fact that such a microscopic explanation for its axioms is not necessary. It works perfectly without it. – CuriousOne Jan 09 '16 at 07:00
  • Note that Noether's theorem relies on a Lagrangian formulation, cf. e.g. this Phys.SE post. – Qmechanic Jan 09 '16 at 07:20

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