Hysteresis

Hysteresis is a property of certain systems in which the state or output depends not only on the present input but also on the history of inputs. When the driving input is varied up and down, the output generally traces a loop rather than retracing the same path, and energy is dissipated in the process.

Hysteresis occurs in several domains: magnetic, mechanical, dielectric, thermal, and biological. Magnetic hysteresis appears in ferromagnetic materials, where magnetization laggs behind the applied magnetic field; the resulting magnetization-field loop has a coercive field and a remanent magnetization, and it is central to transformers, electric machines, and magnetic storage. Mechanical or viscoelastic hysteresis arises from internal friction and time-dependent deformation; the stress-strain response exhibits a loop during loading and unloading, reflecting energy loss and damping. Dielectric and ferroelectric hysteresis involve polarization lagging behind electric field, producing loops that matter for capacitors and memory devices. Thermal hysteresis occurs when phase transitions depend on temperature history, leading to delayed transformations, supercooling or superheating. In biology and chemistry, history-dependent responses can appear in enzyme regulation, receptor signaling, or drug effects where the outcome depends on prior exposure or treatment path.

Modeling approaches include rate-independent and rate-dependent formulations; the Preisach model is a classical framework for hysteresis in magnetism, while other models represent systems with internal state variables and thresholds. Hysteresis is exploited in devices such as magnetic memories and sensors, and it is a source of error to be compensated in precision instruments.