Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the contact geometry and the Poisson geometry of the ideal gas   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.

26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga