Entropy driven atomic motion in laser-excited bismuth

We introduce a thermodynamical model based on the two-temperature approach in order to fully understand the dynamics of the coherent A$_{1g}$ phonon in laser-excited bismuth. Using this model, we simulate the time evolution of (111) Bragg peak intensities measured by Fritz {\it{et al}} [Science {\bf 315}, 633 (2007)] in femtosecond X-ray diffraction experiments performed on a bismuth film for different laser fluences. The agreement between theoretical and experimental results is striking not only because we use fluences very close to the experimental ones but also because most of the model parameters are obtained from {\it{ab-initio}} calculations performed for different electron temperatures.