Lagrangian mechanics and thermodynamics

[Feynmanfan]

Dear friends,

After having studied thermodynamics for some months as well as Lagrangian mechanics, I'm trying to find a relationship between the Hamiltonian, Lagrangian, conjugated potentials etc. and thermodynamic potentials (such as Gibbs free energy, Enthalpy etc.).

I mean, they may have nothing to do with each other but I'm sure there's an analogy. I've learned to do Legendre's transformations in both fields!

Is The analogous of the principle of least action the principle of minimum energy at constant entropy?

I don't know if it's a waste of time trying to find a conexion.

Happy new year!

 

[dextercioby]

To your knowledge,there is a connection between the Hamiltonian (classical or quantum) and thermodynamic quantities which is realized in statistical thermodynamics,which is a subtheory of statistical mechanics who finds the well known results from classical thermodynamics starting from statistical mechanics principles.
Usually,statistical mechanics is built in the Hamilton formalism,just as QM is built in the Hamilton formalism.

Daniel.