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The Antisymmetry of Distortions

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.