An attempt to understand the structure of particles by means of statistical mechanics is presented. This is accomplished by introducing the Gibbs paradox into particle physics. An interacting-particle model results with level density $\rho \mathrm{}\left(m\right)\mathrm{}$ in the range determined by ${\left[\rho \mathrm{}\right(m\left)\right]}^{-1\mathrm{}}=\phi \left(e^{-\beta m}\right)$, $\beta >0\mathrm{}$, and $\rho \mathrm{}\left(m\right)\mathrm{}\le e^{\gamma m\ln m}$, $\gamma >0\mathrm{}$, as $m\to \infty$. This result is to be contrasted to existing free-particle models which give an exponentially increasing mass spectrum.

• Received 18 January 1971

DOI:https://doi.org/10.1103/PhysRevD.4.2432