  Physical systems evolve from one state to another along paths of least energy
barrier. Without a priori knowledge of the energy landscape, multidimensional
search methods aim to find such minimum energy pathways between the initial and
final states of a kinetic process. However in many cases, the user has to
repeatedly provide initial guess paths, thus ensuring that the reliability of
the final result is heavily user-dependent. Recently, the idea of "distortion
symmetry groups" as a complete description of the symmetry of a path has been
introduced. Through this, a new framework is enabled that provides a powerful
means of classifying the infinite collection of possible pathways into a finite
number of symmetry equivalent subsets, and then exploring each of these subsets
systematically using rigorous group theoretical methods. The method is shown to
lead to the discovery of new, previously hidden pathways for the case studies
of bulk ferroelectric switching and domain wall motion in proper and improper
ferroelectrics, as well as in multiferroic switching. This approach is
applicable to a wide variety of physical phenomena ranging from structural,
electronic and magnetic distortions, diffusion, and phase transitions in
materials.
