  The thermodynamic free energy F is calculated for a gas whose particles are
the quantum excitations of a piecewise uniform bosonic string. The string
consists of two parts of length L_I and L_II, endowed with different tensions
and mass densities, adjusted in such a way that the velocity of sound always
equals the velocity of light. The explicit calculation is done under the
restrictive condition that the tension ratio x = T_I/T_II approaches zero.
Also, the length ratio s = L_II/L_I is assumed to be an integer. The expression
for F is given on an integral form, in which s is present as a parameter. For
large values of s, the Hagedorn temperature becomes proportional to the square
root of s.

High Energy Physics - Theory