We consider a Bose gas at density $\rho > 0$, interacting through a repulsive potential $V \in L^2 (\mathbb{ R}^3)$ with scattering length $\mathfrak{ a} > 0$. We prove an upper bound for the free energy of the system, valid at low temperature $T \lesssim \rho \mathfrak{ a}$. Combined with the recent lower bound obtained in \cite{ HabHaiNamSeiTri-23}, our estimate resolves the free energy per unit volume up to and including the Lee--Huang--Yang order $\mathfrak{ a} \rho^2 (\rho \mathfrak{ a}^3)^{ 1/2}$.
Categories: math-ph math.MP