For hard rods of nonzero length in a 1D harmonic trap, every conserved quantity analytic in positions and momenta is a function of total energy and center-of-mass energy.
Chaos and Coarse Graining in Statistical Mechanics
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Absence of hidden analytic conserved quantities in harmonically confined rods
For hard rods of nonzero length in a 1D harmonic trap, every conserved quantity analytic in positions and momenta is a function of total energy and center-of-mass energy.