# Hysteresis

Hysteresis is a phenomenon whereby the value assumed by a quantity dependent on others is determined not only by the instantaneous values of the latter, but also by the values they had assumed previously; in other words, hysteresis is the characteristic of a system to react in delay to applied stresses and in dependence on the previous state. The term, derived from the Greek ὑστέρησις (hystéresis, “delay”), was introduced in the modern sense by James Alfred Ewing in 1890, and is used generally in the theory of dynamical systems, thus not only in physics, but also in biology and economics.

If the response of a system with hysteresis is plotted in a graph as a function of stimulus, a characteristic closed curve is obtained. In a system without hysteresis, the curve forms a single line.

In the presence of hysteresis you get a splitting of the curve: if traveled from left to right you have a path, if traveled in the opposite direction you get another. In many of the physical phenomena in which we have this characteristic we obtain two horizontal lines: one upper and one lower. These represent the saturation limits.

For a system under consideration, as certain conditions vary, one can have a family of curves, ranging from nearly single to a nearly square enclosed area. The amplitude of the enclosed curve is an indication of the magnitude of the hysteresis. The families of curves can be arranged in the third dimension to delimit a three-dimensional shape.

## Hysteresis error

The hysteresis error of a measuring instrument is defined as the maximum difference between the value detected by the transducer when a specific value of the input quantity is applied, by imposing increasing inputs, and the same value obtained by imposing decreasing inputs. In other words, the hysteresis error is given by the maximum difference between the value measured in ascending direction and the respective value measured in a decreasing direction.

Hysteresis represents the history dependence of physical systems. If you push on something, it will yield: when you release, does it spring back completely? If it doesn’t, it is exhibiting hysteresis, in some broad sense. The term is most commonly applied to magnetic materials: as the external field with the signal from the microphone is turned off, the little magnetic domains in the tape don’t return to their original configuration (by design, otherwise your record of the music would disappear!) Hysteresis happens in lots of other systems: if you place a large force on your fork while cutting a tough piece of meat, it doesn’t always return to its original shape: the shape of the fork depends on its history.

## Mechanical hysteresis

Hysteresis is a delay of the effect when the forces acting upon a body are changed (as if from viscosity or internal friction), or lagging in the values of resulting magnetization in a magnetic material (as iron) due to a changing magnetizing force.

Hysteresis is a phenomenon whereby the value assumed by a quantity dependent on others is determined not only by the instantaneous values of the latter but also by the values they had previously assumed; that is, in other words, hysteresis is the characteristic of a system of reacting late to the applied stresses and depending on the previous state.

Ductile materials plasticize with a corresponding kinematic-type work hardening. Assuming that a body is subjected to a uniaxial tensile greater than the yield stress, from the time the material is subjected to unloading and then a compressive stress, the new compressive yield stress will have a lower value.

In performing a calibration, hysteresis is the characteristic of an instrument to provide different values for the same measuring point when it is measured in an increasing and decreasing manner. Typically, in calibration standards, hysteresis is defined as the maximum difference between the values read on an instrument for the same point in the two up and down cycles. In the calibration of a pressure gauge, for example, the difference in values between rising and falling pressure cycles is an indication of the elastic capacity of the instrument’s sensing element.

The deformation of many materials can exhibit hysteresis. For example, plastic materials, after being deformed by a stress, do not return to their initial configuration when the stress is removed, but exhibit residual deformation. For example, this is the phenomenon for which plastic seals in joints degrade after a certain time, and it is also the reason why pressure changes in the human body increase the risk of circulatory diseases such as ischemia or aneurysms.

Even in the mechanics of porous media the same phenomenon is present, since the porosity of a soil depends both on the tensional state to which it is subjected, but also on its past tensional history, in particular the maximum tension to which it has been subjected in its tensional history. If the maximum tension is greater than the current one, the soil is called over-consolidated, and has a lower porosity than the theoretical one expected due to the load acting on it; on the contrary, the soil is called normal-consolidated.

## Thermodynamic hysteresis

In phase transitions, the transition from one state to another does not occur linearly with the energy supplied or absorbed. Hysteresis can be exploited to filter out unwanted signals in control systems, taking into account the recent history of the signal. For example, in thermostatic controls a heating element (a boiler) is turned on when the temperature falls below a value T1 but is not turned off until a temperature T2 greater than the first one is exceeded. This prevents unwanted switching due to inaccuracy and weak fluctuations around a single threshold value.

## Electromagnetic hysteresis

Ferromagnetic materials are characterized by a magnetic induction not expressible as a function of magnetic field. The relation in an isotropic material being scalar since the fields assume the same direction (but not necessarily the same direction), it is representable on a plane where a hysteresis cycle takes place.

Residual induction can be a problem in several applications, for example in the magnetic field it keeps the anchor of a relay attracted when the control signal ceases. Hysteresis is also one of the causes of energy dissipation in variable regime: magnetic in transformers, and electrical in resistors, which is added to the ohmic one. On the other hand in the magnetic field it is the basis of magnetic storage in tapes and hard disks. In these last devices the direction of the residual magnetization represents a bit: 0 or 1. To change the magnetization state it is necessary to know the previous state, according to which varies the field to be applied.

To avoid this problem, a technique called bias is used, which consists in bringing the system to a known value before writing. The same technique is used in audio tape recorders, where sometimes there is a selector for the type of bias to be used depending on the ferromagnetic material used in different types of tape. In electronic circuits the Schmitt Trigger is used, which generates a hysteresis similar in appearance to that generated in magnetic materials. The circuit is used to eliminate the noise present on the signals. It can be realized by discrete components (operational amplifiers or transistors) but it is present on the inputs of many logic circuits of various families (TTL, CMOS, etc.).

It is also possible to simulate hysteresis on an analog input (ADC) connected to a microprocessor (often integrated into it in microcontrollers or embedded systems). In this case the hysteresis is an algorithm in the software or firmware.

## Hysteresis in economy

Some economic systems present hysteresis. For example, in order to begin to export, companies incur sunk costs, i.e. costs that, once incurred, are no longer considered in assessing the profitability of the export activity, thus generating hysteresis in corporate behavior.

In economics, hysteresis is the inability of the unemployment rate to return to its initial level after an adverse shock, even after the shock has been overcome. It is basically given by four main reasons: the “Insider-Outsider” (i.e., the participation in bargaining for work of those who are already employed in order to maintain their jobs); the “discouraged workers” (i.e., individuals who after a period of time without results stop looking for work); the “search and mismatch” (the habit of workers and entrepreneurs to poor results in the search for employment/employment); the “capital stock” (i.e., the low investment caused by the shock that leads to a low level of capital movements).

The phenomenon of hysteresis can also be explained through the use of “efficiency wage theory.”

## Hysteresis in medicine

In medicine, pacemakers are delayed hysteretically to avoid interference with the activity of the sinus node or the heart. The behavior of the isolated lung in which air is insufflated is also hysteretic. The pressure/volume relation obtained in such experimental conditions allows to identify a marked difference in behavior during insufflation and emptying, with much lower pressures at equal volume during emptying than during filling. The same curve can be drawn if, instead of insufflating air into the lung, it is placed in an airtight container, subsequently emptied by means of a pump. The pressures recorded in this way by a manometer, usually water, connected to the pump will be negative.

## Hysteresis in law

Some jurists have transposed the idea of hysteresis to law. According to one orientation, it refers to “international choices that are difficult to reshape in the short term”, from which it would follow that it would be impossible to obtain within copyright rules specifically adapted to the adhesive nature of software. According to another orientation, the development of law would always be slowed down by existing law, so that, especially with reference to the regulation of new technologies, “the law is often obsolete even when it comes into force”; the situation would be aggravated in those systems characterized by lobbying and meticulous negotiation with the protean universe of stakeholders.