  Distortions are ubiquitous in nature. Under perturbations such as stresses,
fields, or other changes, a physical system reconfigures by following a path
from one state to another; this path, often a collection of atomic
trajectories, describes a distortion. Here we introduce an antisymmetry
operation called distortion reversal, 1*, that reverses a distortion pathway.
The symmetry of a distortion pathway is then uniquely defined by a distortion
group involving 1*; it has the same form as a magnetic group that involves time
reversal, 1'. Given its isomorphism to magnetic groups, distortion groups could
potentially have commensurate impact in the study of distortions as the
magnetic groups have had in the study of magnetic structures. Distortion
symmetry has important implications for a range of phenomena such as structural
and electronic phase transitions, diffusion, molecular conformational changes,
vibrations, reaction pathways, and interface dynamics.
