histerese

Hysteresis, sometimes spelled histerese in some languages, is a phenomenon in which the output of a system depends on its history as well as its current input. As a result, the relation between input and output traces a loop when the input is cycled, rather than retracing the same path. Hysteresis arises from memory effects in materials, friction, thresholds, or phase transitions.

In magnetism, magnetic hysteresis describes how magnetization M responds to applied field H. As H increases and decreases, M lags, forming a loop. Key characteristics are coercivity (the field needed to reduce magnetization to zero) and remanence (residual magnetization). Materials with strong hysteresis include ferromagnets and ferrites.

Different contexts exhibit hysteresis. In mechanics and materials science, stress-strain curves of viscoelastic or plastic materials show loading-unloading loops, with energy dissipated as heat. In electronics, ferroelectric, piezoelectric, and some memristive devices show dielectric or conductivity hysteresis; Schmitt trigger devices use hysteresis to create noise-immune switching. Some phase transformations display thermal hysteresis, with different transition temperatures upon heating and cooling.

Hysteresis is modeled using mathematical formalisms such as rate-independent models and memory-based constructs like the Preisach or Prandtl–Ishlinskii models, Bouc–Wen for structural damping, and various state-space representations. It is studied in physics, engineering, biology, economics, and ecology as a descriptor of systems with memory and path dependence.