Eccentricity and inclination PDFs of the solar system inner planets. The PDFs of L08 are plotted in solid lines at three different times, t = 500 Myr, 2.5 Gyr, and 5 Gyr, to illustrate chaotic diffusion (the PDF broadens and its peak decreases as time increases; the inclination PDFs are not the original PDFs, but the Rice distributions fitted by Laskar, see Sect. 3 for explanations). The PDFs predicted by the microcanonical ensemble of the Laplace-Lagrange theory, Eq. (16), are shown in dashed line. The inclinations are computed with respect to the J2000 ecliptic.