Hysteresis describes systems where the current state is shaped by both past and present influences. Notable for its path dependence and non-linearity, the concept is particularly relevant in disciplines such as material science, engineering, and economics.


Hysteresis: Phenomenon where the current state of a system depends on both its current input and past states.

Types and Qualitative Differences

  • Mechanical: Found in materials like rubber bands, characterized by elastic energy loss.
  • Magnetic: Seen in ferromagnetic materials such as iron, involves magnetic field alignment.
  • Electrical: Present in systems like capacitors, related to charge storage.
  • Thermal: Observed in phase transitions, such as the melting of ice.
  • Biological: Manifests in physiological processes like neuron firing.

Mathematical Models

  • First-Order Systems: Described by the ordinary differential equation \( \frac{dy}{dt} = f(y, u, t) \).
  • Higher-Order Systems: Captured by systems of ordinary or partial differential equations.

Key Parameters

  • Threshold: Value at which the system changes state.
  • Memory: Reflects how past states influence the current state.
  • Rate-Dependence: Indicates the speed at which a system returns to equilibrium.
  • Time-Dependence: Hysteresis is often a time-dependent phenomenon.

Distinctive Features

  • Path Dependence: Response is tied to the history of inputs.
  • Non-Linearity: The system does not adhere to the principle of superposition.
  • Asymmetry: Responses to increasing and decreasing inputs differ.
  • Energy Dissipation: Energy is usually lost in a hysteresis loop, crucial for understanding efficiency in various applications.
  • Scale Invariance: In some systems, hysteresis manifests across multiple scales.


Derived from the Greek word “hysteresis,” meaning “deficiency” or “lagging behind.”


  • Electric Motors: Design critically relies on understanding magnetic hysteresis and energy dissipation.
  • Seismology: Earthquake understanding enhanced by mechanical hysteresis and scale invariance.
  • Medicine: Hysteresis concepts relevant to drug dosing and metabolic rate calculations.

Relevant Academic Fields

  • Physics: Material properties, energy dissipation, and quantum mechanics.
  • Engineering: Control systems, energy efficiency, and materials science.
  • Economics: Labor market and consumer behavior models often include hysteresis effects.

Related Concepts

  • Feedback Loops: Can induce hysteresis phenomena.
  • Rate-Independent: A subset where the effect of rate-dependence is negligible.

Common Misunderstandings

Not Inertia: Unlike inertia, hysteresis involves memory of past states.