Classical Lagrangian Model of the Pauli Principle

A classical Lagrangian model of the Pauli potential is introduced. It is shown that the kinematic kinetic energy ($\sum \frac{1}{2} m v^2$) in the model approximately reproduces the energy of a free Fermi gas at low temperatures and at densities relevant in nuclear collisions with moderate beam energies. Differences between canonical and kinematic quantities are pointed out. The Pauli potential can be used in transport simulations.