Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamilton-Jacobi formalism for string gas thermodynamics   We show that the thermodynamics of a system of strings at high energy
densities under the ideal gas approximation has a formulation in terms of
Hamilton-Jacobi theory. The two parameters of the system, which have dimensions
of energy density and number density, respectively, define a family of
hypersurfaces of co-dimension one, which can be described by the vanishing of a
function F that plays the role of a Hamiltonian.

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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
3
The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: econ
5
The categories of this paper are: gr-qc