There is a celebrated energy equipartition theorem, it works fine for many systems. But it requires the dense filling of the surface of constant energy. What if there are other conserved quantities, like momentum or angular momentum? It seems, that the energy partitioning will be uneven, with approximately linear dependence of the mean energy on the mass share, associated with the degree of freedom. The heavier the particle, the lesser it's mean energy. There are numerical pieces of evidence of such partitioning in different systems, like isolated clusters of atoms. A good example is the usual ideal gas in a round vessel (PDF). That recently published paper of mine contains the exact law, but only for a particular system.

The question is, how general are such laws of uneven energy partitioning?

Can anyone provide other examples of uneven partitioning laws?



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