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.

 

[Graeme Robinson]

Dear ,

Thank you for sharing your thoughts on the relationship between Lagrangian mechanics and thermodynamics. It is indeed an interesting topic to explore and I believe there is a connection between the two fields.

One possible way to understand this connection is through the concept of energy minimization. In Lagrangian mechanics, we use the principle of least action to determine the path of a system that minimizes the action. Similarly, in thermodynamics, we use the principle of minimum energy to determine the equilibrium state of a system that minimizes the energy at constant entropy.

Moreover, the Lagrangian and Hamiltonian formalisms can be related to thermodynamic potentials through Legendre transformations. For example, the Lagrangian can be seen as a Legendre transformation of the Hamiltonian, and the Helmholtz free energy can be obtained from the Hamiltonian through a Legendre transformation with respect to the energy variable.

In fact, there have been several studies on the application of Lagrangian mechanics to thermodynamic systems, such as in the study of phase transitions and critical phenomena. This further supports the idea that there is a connection between the two fields.

In conclusion, I don't think it's a waste of time to explore the relationship between Lagrangian mechanics and thermodynamics. It can provide a deeper understanding of both fields and potentially lead to new insights and applications. Happy new year to you too!