Free fluid vesicles are not exactly spherical

At finite temperature, vesicles perform small fluctuations around an average shape. In the limit of low temperature or high bending rigidity, the fluctuations vanish and the vesicle approaches the energetically favored configuration. In the absence of a volume constraint the configuration of lowest energy is a perfect sphere. It is often assumed that the spherical shape is also the most probable shape for finite temperatures. Consequently, a force would have to be applied to make the average shape of the vesicle anisotropic. In this article it is shown that these assumptions are incorrect. At finite temperature, the most probable shapes of a vesicle without volume constraint are prolate or oblate, where the probability for prolate shapes is slightly larger. For larger deviations from the sphere the vesicle behaves as expected. The behavior at small deformations that is found for vesicles without volume constraint as well as in the presence of a finite osmotic pressure is basically an entropic effect. It already occurs in a three-dimensional crossed dumbbells model system. In two dimensions the same model favors the isotropic state.