Is there any relation between the two decompositions?

- Evidence lower bound that decomposes into Energy term and Neg-Entropy term.

- Hamiltonian that decomposes into potential and kinetic energy

w, z, x are parameter, latent variable, observed data in the first equation from this paper.

\rho and \theta are auxiliary momentum variable and parameter from stan manual.

The structural similarity of R.H.S of both equations and the term ‘energy’ led me to be curious on their relations. Any opinion would be appreciated!

One more tangential question on latent parameter and variable. According to this, a parameter is fixed but unknown; would it be better to name w as a variable rather than parameter? Or since w is actually a function according to the following equation in this paper, it is fixed and parameter is correct?