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 $\ensuremath{\rho}(m)$ in the range determined by ${[\ensuremath{\rho}(m)]}^{\ensuremath{-}1}=\ensuremath{\varphi}({e}^{\ensuremath{-}\ensuremath{\beta}m})$, $\ensuremath{\beta}g0$, and $\ensuremath{\rho}(m)\ensuremath{\le}{e}^{\ensuremath{\gamma}m\mathrm{ln}m}$, $\ensuremath{\gamma}g0$, as $m\ensuremath{\rightarrow}\ensuremath{\infty}$. This result is to be contrasted to existing free-particle models which give an exponentially increasing mass spectrum.