We consider a reverse process of relaxation and obtain a necessary condition under which the reverse process proceeds. Applying this method to fluid vesicle dynamics, which is derived by Onsager's variational principle, we derive the necessary equations for spontaneous curvature and anisotropic bending rigidity distributions that are induced by the proteins attached to the membrane of the vesicle. Numerical schemes to obtain the distributions of the protein properties are proposed and applied to spheroid vesicles. It is shown that proteins with an anisotropic spontaneous curvature deviator are effective in forming a long prolate spheroid. We conclude that the proposed method may become a useful tool to study the protein distribution in the membrane of a vesicle with a measured shape.