Hamilton-Jacobi formalism for string gas thermodynamics

TL;DR

This paper introduces a Hamilton-Jacobi framework to describe the thermodynamics of high-energy string gases, providing a new mathematical perspective on their thermodynamic properties.

Contribution

It formulates string gas thermodynamics using Hamilton-Jacobi theory, linking thermodynamic parameters to a Hamiltonian function, which is a novel approach in this context.

Findings

Thermodynamics of string gases can be described by Hamilton-Jacobi equations.

The parameters define hypersurfaces characterized by a Hamiltonian function.

Provides a new geometric perspective on string gas thermodynamics.

Abstract

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.