An all-atom theory of viral structural transitions (STs) is developed based on a multiscale analysis of the N-atom Liouville equation. The approach yields an understanding of viral STs from first principles and a calibrated interatomic force field. To carry out the multiscale analysis, we introduce slow variables characterizing the whole-virus dynamics. Use of the "nanocanonical ensemble" technique and the fundamental hypothesis of statistical mechanics (i.e., the equivalence of long-time and ensemble averages) is shown to imply a Fokker-Planck equation yielding the coarse-grained evolution of the slow variables. As viral STs occur on long time scales, transition state theory is used to estimate the energy barrier of transition between free energy wells implied by observed hysteresis in viral STs. Its application to Nudaurelia capensis omega virus provides an upper bound on the free energy barrier when a single dilatational order parameter is used. The long time scale of viral STs is shown to follow from the aggregate effect of inertia, energy barrier, and entropic effects. Our formulation can be generalized for multiple order parameter models to account for lower free energy barrier pathways for transition. The theory with its all-atom description can be applied to nonviral nanoparticles as well.