  We elaborate on existing notions of contact geometry and Poisson geometry as
applied to the classical ideal gas. Specifically we observe that it is possible
to describe its dynamics using a 3-dimensional contact submanifold of the
standard 5-dimensional contact manifold used in the literature. This reflects
the fact that the internal energy of the ideal gas depends exclusively on its
temperature. We also present a Poisson algebra of thermodynamic operators for a
quantum-like description of the classical ideal gas. The central element of
this Poisson algebra is proportional to Boltzmann's constant. A Hilbert space
of states is identified and a system of wave equations governing the
wavefunction is found. Expectation values for the operators representing
pressure, volume and temperature are found to satisfy the classical equations
of state.
