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I would like to learn more about "unnatural" Hamiltonian systems, that is, systems whose energies cannot be written as

$$H(p,q) = K(q) + U(p).$$

I have seen the term "natural" applied to systems that can be separated into kinetic and potential components, but have only come across the term "unnatural" in a few scattered documents online. An example is discussed in this very interesting paper on the Kuramoto model.

I am particularly interested in techniques for sampling from the associated Gibbs distribution $f(p,q) = e^{-H(p,q)}$. Any pointers will be greatly appreciated.

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    $\begingroup$ This post (v3) seems too broad. $\endgroup$
    – Qmechanic ♦
    Commented Feb 12, 2020 at 13:13

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