Pressure of a dilute spin-polarized Fermi gas: Upper bound

Abstract

We prove an upper bound on the pressure of a dilute fully spin-polarized Fermi gas capturing the leading correction to the pressure of a free gas resulting from repulsive interactions. This correction is of order $a^3\rho^{8/3}$, with $a$ the $p$-wave scattering length of the interaction and $\rho$ the particle density, depends on the temperature and matches the corresponding lower bound of [arXiv:2307.01113].