16 questions linked to/from Physical meaning of Legendre transformation
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### Is there a physical connection between Lagrangian mechanics and Hamilton mechanics [duplicate]

I know that the Hamilton's equations results from the Legendre transformation of the Lagrange equation. It's also well-known that the Hamiltonian is equal to the energy of a system if the system is ...
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### Why are so many (all?) Key concepts in thermodynamics derived from a legendre transformation? [duplicate]

Given a function $f(x,y)$, a legendre transform w.r.t. $x$ is $f^*(p,y)=p x - f(x,y) |_{p=\frac {\partial f(x,y)}{\partial x}}$. E.g. , the various free energies, enthalpy, etc are all legendre ...
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