One of the most prominent examples showcasing the close ties between global optimization processes and statistical physics is the simulated annealing method, rooted in the Metropolis-Hasting sampling approach. In this talk, we emphasize the close connections between the underlying stochastic dynamics and linear Boltzmann equations and how convergence to the global minimum can be related to classical entropy inequalities. This allows us to reinterpret classical results, such as the connections between simulated annealing and mean-field Langevin dynamics, and to derive enhanced algorithms based on different strategies to control the annealing process.