  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.
