perturb

Perturb is a verb meaning to disturb or modify something slightly, often in a way that changes subsequent behavior or outcomes. It can describe a range of disturbances, from a gentle disruption of order to a controlled alteration of a system’s parameters. In technical contexts, perturbation refers to the deviation from an ideal state or baseline.

Etymology: Perturb derives from Latin perturbare, from per- "through, thoroughly" and turbare "to confuse, disturb." The word entered English in the late medieval period and has retained its sense of disturbance and modification.

In science and engineering, perturbation plays a central role. Perturbation theory provides a framework to approximate complex problems by starting from a solvable, simple case and adding a small perturbation. Solutions are often expressed as series in a small parameter, capturing how slight changes influence outcomes. This method is widely used in quantum mechanics, quantum field theory, celestial mechanics, fluid dynamics, and other disciplines. In dynamical systems and control, perturbations describe external inputs or disturbances that push a system away from its nominal trajectory, and perturbation analysis assesses stability and sensitivity.

In statistics, data perturbation refers to intentional modifications of data to protect privacy or to test robustness. In machine learning, perturbations of inputs—adversarial perturbations—can cause models to err, prompting development of defenses and robust training methods.

See also perturbation, disturbance, stability, and perturbation theory.