preprint draft Andreas Deuchert author 4DA65CD0-F248-11E8-B48F-1D18A9856A870000-0003-3146-6746 Simon Mayer author 30C4630A-F248-11E8-B48F-1D18A9856A87 Robert Seiringer author 4AFD0470-F248-11E8-B48F-1D18A9856A870000-0002-6781-0521 RoSe department Analysis of quantum many-body systems project 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 $\rho$ and inverse temperature $\beta$ differs from the one of the non-interacting system by the correction term $4 \pi \rho^2 |\ln a^2 \rho|^{-1} (2 - [1 - \beta_{\mathrm{c}}/\beta]_+^2)$. Here $a$ is the scattering length of the interaction potential, $[\cdot]_+ = \max\{ 0, \cdot \}$ and $\beta_{\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless critical temperature for superfluidity. The result is valid in the dilute limit $a^2\rho \ll 1$ and if $\beta \rho \gtrsim 1$. 2019 eng 1910.0337210.48550/arXiv.1910.03372 61 https://research-explorer.ista.ac.at/record/7790 https://research-explorer.ista.ac.at/record/7514 Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv, 1910.03372. A. Deuchert, S. Mayer, R. Seiringer, ArXiv (n.d.). Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/arXiv.1910.03372">https://doi.org/10.48550/arXiv.1910.03372</a>. Deuchert, A., Mayer, S., &#38; Seiringer, R. (n.d.). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.1910.03372">https://doi.org/10.48550/arXiv.1910.03372</a> A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” <i>arXiv</i>. . Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>ArXiv</i>, 1910.03372, doi:<a href="https://doi.org/10.48550/arXiv.1910.03372">10.48550/arXiv.1910.03372</a>. Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/arXiv.1910.03372">10.48550/arXiv.1910.03372</a> 75242020-02-26T08:46:40Z2026-04-08T07:25:40Z