The free energy of the two-dimensional dilute Bose gas. I. Lower bound Deuchert, Andreas ; https://orcid.org/0000-0003-3146-6746 Mayer, Simon Seiringer, Robert ; https://orcid.org/0000-0002-6781-0521 ddc:510 We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density 𝜌 and inverse temperature 𝛽 differs from the one of the noninteracting system by the correction term 𝜋𝜌𝜌𝛽𝛽 . Here, is the scattering length of the interaction potential, and 𝛽 is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit 𝜌 and if 𝛽𝜌 . Cambridge University Press 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/7790 https://research-explorer.ista.ac.at/download/7790/7797 Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. 2020;8. doi:<a href="https://doi.org/10.1017/fms.2020.17">10.1017/fms.2020.17</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1017/fms.2020.17 info:eu-repo/semantics/altIdentifier/e-issn/2050-5094 info:eu-repo/semantics/altIdentifier/wos/000527342000001 info:eu-repo/semantics/altIdentifier/arxiv/1910.03372 https://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess