The article highlights the importance of beta convergence and generative artificial intelligence in facilitating the transition to a more generative paradigm. A panel data of 120 countries between 2007 and 2022 is used to estimate the effect of the Logistics Performance Index (LPI) on economic growth, along with other variables such as human capital, physical capital and employment. The results show that the most significant LPI indices are Customs, Infrastructure and competitive international shipping prices, and that logistics has facilitated convergence in the growth of less developed countries. It is concluded that conditional beta convergence has allowed for an inverse relationship between the growth trend and the income level of each starting country, indicating that conditional convergence exists and that logistics has played a key role in facilitating economic convergence between less developed and developed countries. Overall, the results of the study provide valuable information for policy makers in formulating appropriate strategies to promote global economic growth. In summary, beta convergence and technologies such as generative artificial intelligence are important tools to facilitate the transition to a more generative paradigm in logistics performance in countries around the world.