The free energy of the two-dimensional dilute Bose gas. II. Upper bound Mayer, Simon Seiringer, Robert ; https://orcid.org/0000-0002-6781-0521 We prove an upper bound on the free energy of a two-dimensional homogeneous Bose gas in the thermodynamic limit. We show that for a2ρ ≪ 1 and βρ ≳ 1, the free energy per unit volume differs from the one of the non-interacting system by at most 4πρ2|lna2ρ|−1(2−[1−βc/β]2+) to leading order, where a is the scattering length of the two-body interaction potential, ρ is the density, β is the inverse temperature, and βc is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. In combination with the corresponding matching lower bound proved by Deuchert et al. [Forum Math. Sigma 8, e20 (2020)], this shows equality in the asymptotic expansion. AIP Publishing 2020 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/8134 Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. II. Upper bound. <i>Journal of Mathematical Physics</i>. 2020;61(6). doi:<a href="https://doi.org/10.1063/5.0005950">10.1063/5.0005950</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1063/5.0005950 info:eu-repo/semantics/altIdentifier/issn/0022-2488 info:eu-repo/semantics/altIdentifier/wos/000544595100001 info:eu-repo/semantics/altIdentifier/arxiv/2002.08281 info:eu-repo/semantics/openAccess