Hysteresis

Hysteresis is a phenomenon where the current state of a system depends on its history. In many systems, the output does not respond immediately or identically to an input. Instead, the system "remembers" what happened to it previously. This dependence on the past means that if you change an input and then change it back, the system might not return to its original state. This behavior is often visualized using a hysteresis loop.

A plot of a single component of the system's moment often forms this loop. These loops show that different values of one variable can exist for the same value of another variable, depending on the direction of change.

There are two primary ways to categorize this behavior: rate-dependent and rate-independent. Rate-dependent hysteresis involves a dynamic lag between an input and an output. This lag is tied to how fast the input changes. For example, a sinusoidal input might result in a sinusoidal output that experiences a phase lag. If the input is reduced to zero, the output eventually decays to zero as well. This creates a limited memory of the past. In these systems, the phase lag often disappears if the input is varied more slowly. This type of hysteresis is frequently associated with energy dissipation, such as power loss caused by friction.

Rate-independent hysteresis is different because it creates a persistent memory. In these systems, the future state depends on the history of states visited, but this memory does not fade as events recede into the past. If an input variable cycles from one value to another and back again, the output may be at a different value upon its return. The specific values depend on the path taken through the variables, not the speed of the traversal. Many scientists restrict the term hysteresis specifically to this rate-independent type. This lasting memory is what allows for stable data storage in technologies like hard disk drives.

One of the most common examples of hysteresis is found in elastic materials like rubber. This is known as elastic hysteresis. If you hang a rubber band and add weights, it stretches under the force. When you remove the weights, the band contracts. However, the band does not follow the same path during unloading as it did during loading.

The rubber band is actually harder to stretch than it is to let it contract. This occurs because of internal friction within the material. This friction converts some of the mechanical energy into thermal energy, or heat. This is why a rubber band can feel warm when stretched quickly and cool when suddenly released.

Engineers intentionally use hysteresis to make systems more stable and reliable. In control systems, it can be used to filter signals. A thermostat is a perfect example of this application. To prevent a heater from switching on and off too rapidly, a thermostat uses different thresholds. It might turn the heater on when the temperature drops below 18 °C, but it will not turn it off until the temperature rises above 22 °C.

This gap prevents unwanted frequent switching caused by small fluctuations. Similarly, electronic circuits called Schmitt triggers use hysteresis to compensate for electrical noise or contact bounce in switches.

The history of the term "hysteresis" traces back to Ancient Greek, where it meant "deficiency" or "lagging behind." The term was officially coined in 1881 by Sir James Alfred Ewing to describe the behavior of magnetic materials. Early mechanical studies of these systems were conducted by James Clerk Maxwell. Later, researchers like Ferenc Preisach developed mathematical models to explain these complex behaviors. The Preisach model was originally applied to ferromagnetism. Other scientists, such as Louis Néel and Douglas Hugh Everett, contributed significantly to our understanding of magnetism and absorption. In the 1970s, a group of Russian mathematicians led by Mark Krasnosel'skii developed a more formal mathematical theory for hysteretic systems.

Hysteresis is a fundamental concept that connects many different scientific fields. It appears in physics through magnetism and in chemistry during phase transitions. In engineering, it is vital for designing everything from vehicle suspensions to micropositioning control. It even appears in biology and economics. In aerodynamics, hysteresis can be observed in how air flows over a wing during a stall. In hydraulics, it can affect how river flows change during a flood wave. Because these systems are nonlinear, they can be mathematically challenging to model, but they are essential to how the physical world functions.