  We show that it is possible to consistently describe dynamical systems, whose
equations of motion are of degree higher than two, in the microcanonical
ensemble, even if the higher derivatives aren't coordinate artifacts. Higher
time derivatives imply that there are more than one Hamiltonians, conserved
quantities due to time translation invariance, and, if the volume in phase
space, defined by their intersection, is compact, microcanonical averages can
be defined and there isn't any instability, in the sense of Ostrogradsky, even
though each Hamiltonian, individually, may define a non-compact (hyper)surface.
  We provide as concrete example of these statements the Pais--Uhlenbeck
oscillator and show that it can describe a system that makes sense in the
microcanonical ensemble. It describes two oscillators that are coupled by
imposing a fixed phase difference, that thereby describes a non--local
interaction between them. The consistent quantum dynamics can straightforwardly
be expressed using two pairs of creation and annihilation operators, with the
phase difference describing a flux, that describes the interaction.
  The properties of the action imply that particular solutions, that would
describe independent oscillators, are, in general, not admissible.The reason is
that the coordinate transformation, that would decouple the oscillators isn't a
symmetry of the action--unless a "BPS bound" is saturated. Only then do they
decouple. But, in these cases, the action does describe one, not two,
oscillators, anyway and the higher derivative term is a coordinate artifact.
