Hysteresis is the dependence of a system not just on its current environment but also on its past. This dependence arises because the system can be in more than one internal state. To predict its future evolution, either its internal state or its history must be known. If a given input alternately increases and decreases, the output tends to form a loop as in Fig. 1. However, loops may also occur because of a dynamic lag
Lag is a common word meaning to fail to keep up or to fall behind. In real-time applications, the term is used when the application fails to respond in a timely fashion to inputs...

 between input and output.
Hysteresis is the dependence of a system not just on its current environment but also on its past. This dependence arises because the system can be in more than one internal state. To predict its future evolution, either its internal state or its history must be known. If a given input alternately increases and decreases, the output tends to form a loop as in Fig. 1. However, loops may also occur because of a dynamic lag
Lag is a common word meaning to fail to keep up or to fall behind. In real-time applications, the term is used when the application fails to respond in a timely fashion to inputs...

 between input and output. Often, this effect is also referred to as hysteresis, or rate-dependent hysteresis. This effect disappears as the input changes more slowly, so many experts do not regard it as true hysteresis.

Hysteresis occurs in ferromagnetic materials and ferroelectric
Ferroelectricity is a property of certain materials which possess a spontaneous electric polarization that can be reversed by the application of an external electric field. The term is used in analogy to ferromagnetism, in which a material exhibits a permanent magnetic moment. Ferromagnetism was...

 materials, as well as in the deformation
Deformation (mechanics)
Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration. A configuration is a set containing the positions of all particles of the body...

 of some materials (such as rubber band
Rubber band
A rubber band is a short length of rubber and latex formed in the shape of a loop and is commonly used to hold multiple objects together...

s and shape-memory alloys) in response to a varying force. In natural systems hysteresis is often associated with irreversible thermodynamic change. Many artificial systems are designed to have hysteresis: for example, in thermostat
A thermostat is the component of a control system which regulates the temperature of a system so that the system's temperature is maintained near a desired setpoint temperature. The thermostat does this by switching heating or cooling devices on or off, or regulating the flow of a heat transfer...

s and Schmitt triggers, hysteresis is produced by positive feedback
Positive feedback
Positive feedback is a process in which the effects of a small disturbance on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system that responds to a perturbation in a way that reduces its effect is...

 to avoid unwanted rapid switching. Hysteresis has been identified in many other fields, including economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

 and biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...



The term "hysteresis" is derived from , an ancient Greek
Ancient Greek
Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...

 word meaning "deficiency" or "lagging behind". It was coined by Sir James Alfred Ewing
James Alfred Ewing
Sir James Alfred Ewing KCB FRS FRSE MInstitCE was a Scottish physicist and engineer, best known for his work on the magnetic properties of metals and, in particular, for his discovery of, and coinage of the word, hysteresis.It was said of Ewing that he was 'Careful at all times of his appearance,...


Some early work on describing hysteresis in mechanical systems was performed by James Clerk Maxwell
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...

. Subsequently, hysteretic models have received significant attention in the works of Ferenc Preisach (Preisach model of hysteresis
Preisach model of hysteresis
The Preisach model of hysteresis generalizes hysteresis loops as the parallel connection of independent relay hysterons. It was first suggested in 1935 by Ferenc Preisach in the German academic journal "Zeitschrift für Physik". Since then, it has become a widely accepted model of hysteresis...

), Louis Néel and D. H. Everett in connection with magnetism and absorption. A more formal mathematical theory of systems with hysteresis was developed in 1970s by a group of Russian mathematicians led by Mark Krasnosel'skii
Mark Krasnosel'skii
Mark Alexandrovich Krasnosel'skii was a Soviet, Russian and Ukrainian mathematician renowned for his work on nonlinear functional analysis and its applications.- Early years :...

, one of the founders of nonlinear analysis. He suggested an investigation of hysteresis phenomena using the theory of nonlinear operators.


The meaning of hysteresis closest to its etymology
Etymology is the study of the history of words, their origins, and how their form and meaning have changed over time.For languages with a long written history, etymologists make use of texts in these languages and texts about the languages to gather knowledge about how words were used during...

 is a lag
Lag is a common word meaning to fail to keep up or to fall behind. In real-time applications, the term is used when the application fails to respond in a timely fashion to inputs...

 between input and output. A simple example would be a sinusoidal input and output that are separated by a phase lag :
Such behavior can occur in linear systems, and a more general form of response is
where is the instantaneous response and is the response
Impulse response
In signal processing, the impulse response, or impulse response function , of a dynamic system is its output when presented with a brief input signal, called an impulse. More generally, an impulse response refers to the reaction of any dynamic system in response to some external change...

 at time to an impulse at time . In the frequency domain
Frequency domain
In electronics, control systems engineering, and statistics, frequency domain is a term used to describe the domain for analysis of mathematical functions or signals with respect to frequency, rather than time....

, input and output are related by a complex generalized susceptibility.

This kind of hysteresis is often referred to as rate-dependent hysteresis. If the input is reduced to zero, the output has a transient
Transience means passing with time or is the state of being brief and short-lived. Something which has the property of transience is said to be transient, or often simply a transient or transient state.Examples include:* Transient...

 response. This constitutes a memory of the past, but a limited one because it disappears as the transient decays to zero. The phase lag depends on the frequency of change in the input, and goes to zero as the frequency decreases.

In physical systems, rate-dependent hysteresis is often due to dissipative effects like friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

 and is associated with power loss.


Systems with rate-independent hysteresis have a persistent memory of the past that remains after the transients have died out. The future evolution of such a system depends on the past. If an input variable cycles from to and back, the output may be initially and a different value on the return. The values of depend on the values that passes through, but not on the rate of change of . Many authors define hysteresis as rate-independent hysteresis.

Control systems

Hysteresis can be used to filter signals so that the output reacts slowly by taking recent history into account. For example, a thermostat
A thermostat is the component of a control system which regulates the temperature of a system so that the system's temperature is maintained near a desired setpoint temperature. The thermostat does this by switching heating or cooling devices on or off, or regulating the flow of a heat transfer...

 controlling a heater may turn the heater on when the temperature drops below A degrees, but not turn it off until the temperature rises above B degrees (e.g., if one wishes to maintain a temperature of 20 °C, then one might set the thermostat to turn the furnace on when the temperature drops below 18 °C, and turn it off when the temperature exceeds 22 °C). This thermostat has hysteresis. Thus the on/off output of the thermostat to the heater when the temperature is between A and B depends on the history of the temperature. This prevents rapid switching on and off as the temperature drifts around the set point. The furnace is either off or on, with nothing in between. The thermostat is a system; the input is the temperature, and the output is the furnace state. If the temperature is 21 °C, then it is not possible to predict whether the furnace is on or off without knowing the history of the temperature.

Similarly a pressure switch also exhibits hysteresis. Its pressure setpoints are substituted for those of temperature corresponding to a thermostat.

Electronic circuits

A Schmitt trigger is a simple electronic circuit that also exhibits this property. Often, some amount of hysteresis is intentionally added to an electronic circuit to prevent unwanted rapid switching. This and similar techniques are used to compensate for contact bounce in switches, or noise in an electrical signal.

A latching relay uses a solenoid to actuate a ratcheting mechanism that keeps the relay closed even if power to the relay is terminated.

Hysteresis is essential to the workings of some memristor
Memristor is a passive two-terminal electrical component envisioned by Leon Chua as a fundamental non-linear circuit element relating charge and magnetic flux linkage...

s (circuit components which "remember" changes in the current passing through them by changing their resistance).

The hysteresis effect can be used when connecting complex circuits with the so-called passive matrix addressing
Passive matrix addressing
Passive matrix addressing is an addressing scheme used in earlier LCD displays, and may be used in future LCD displays. This is a matrix addressing scheme meaning that only m + n control signals are required to address a m × n display...

. This scheme is praised as a technique that can be used in modern nanoelectronics, electrochrome cells, memory effect
Memory effect
Memory effect, also known as battery effect, lazy battery effect or battery memory, is an alleged effect observed in nickel cadmium rechargeable batteries that causes them to hold less charge...

, etc. In this scheme, shortcuts are made between adjacent components (see crosstalk) and the hysteresis helps to keep the components in a particular state while the other components change states. That is, one can address all rows at the same time instead of doing each individually.

In the field of audio electronics, a noise gate
Noise gate
A Noise Gate or gate is an electronic device or software that is used to control the volume of an audio signal. In its most simple form, a noise gate allows a signal to pass through only when it is above a set threshold: the gate is 'open'. If the signal falls below the threshold no signal is...

 often implements hysteresis intentionally to prevent the gate from "chattering" when signals close to its threshold are applied.

User interface design

A hysteresis is sometimes intentionally added to computer algorithms. The field of user interface design
User interface design
User interface design or user interface engineering is the design of computers, appliances, machines, mobile communication devices, software applications, and websites with the focus on the user's experience and interaction...

 has borrowed the term hysteresis to refer to times when the state of the user interface intentionally lags behind the apparent user input. For example, a menu that was drawn in response to a mouse-over event may remain on-screen for a brief moment after the mouse has moved out of the trigger region and the menu region. This allows the user to move the mouse directly to an item on the menu, even if part of that direct mouse path is outside of both the trigger region and the menu region. For instance, right-clicking on the desktop in most Windows interfaces will create a menu that exhibits this behavior.

Elastic hysteresis

In the elastic hysteresis of rubber, the area in the centre of a hysteresis loop is the energy dissipated due to material plasticity.

Elastic hysteresis was one of the first types of hysteresis to be examined.

A simple way to understand it is in terms of a rubber band with weights attached to it. If the top of a rubber band is hung on a hook and small weights are attached to the bottom of the band one at a time, it will get longer. As more weights are loaded onto it, the band will continue to extend because the force the weights are exerting on the band is increasing. When each weight is taken off, or unloaded, it will get shorter as the force is reduced. As the weights are taken off, each weight that produced a specific length as it was loaded onto the band now produces a slightly longer length as it is unloaded. This is because the band does not obey Hooke's law
Hooke's law
In mechanics, and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law...

 perfectly. The hysteresis loop of an idealized rubber band is shown in Fig. 3.

In one sense the rubber band was harder to stretch when it was being loaded than when it was being unloaded. In another sense, as one unloads the band, the cause (the force of the weights) lags behind the effect (the length) because a smaller value of weight produces the same length. In another sense more energy was required during the loading than the unloading; that energy must have gone somewhere, it was dissipated or "lost" as heat.

Elastic hysteresis is more pronounced when the loading and unloading is done quickly than when it is done slowly. Some materials such as hard metals don't show elastic hysteresis under a moderate load, whereas other hard materials like granite and marble do. Materials such as rubber exhibit a high degree of elastic hysteresis.

A word of caution: rubber behaves like a gas. When the rubber band is stretched it heats up. If it is suddenly released, the rubber cools down, very easy to perceive just by touching.
So, there is a large hysteresis from the thermal exchange with the environment and a smaller hysteresis due to internal friction within the rubber. This proper, intrinsic hysteresis
could be measured only if adiabatic isolation of the rubber band is imposed.

Small vehicle suspensions using rubber
Natural rubber, also called India rubber or caoutchouc, is an elastomer that was originally derived from latex, a milky colloid produced by some plants. The plants would be ‘tapped’, that is, an incision made into the bark of the tree and the sticky, milk colored latex sap collected and refined...

 (or other elastomer
An elastomer is a polymer with the property of viscoelasticity , generally having notably low Young's modulus and high yield strain compared with other materials. The term, which is derived from elastic polymer, is often used interchangeably with the term rubber, although the latter is preferred...

s) can achieve the dual function of springing and damping because rubber, unlike metal springs, has pronounced hysteresis and does not return all the absorbed compression energy on the rebound. Mountain bike
Mountain bike
A mountain bike or mountain bicycle is a bicycle created for off-road cycling. This activity includes traversing of rocks and washouts, and steep declines,...

s have frequently made use of elastomer suspension, as did the original Mini
The Mini is a small car that was made by the British Motor Corporation and its successors from 1959 until 2000. The original is considered a British icon of the 1960s, and its space-saving front-wheel-drive layout influenced a generation of car-makers...


Contact angle hysteresis

The contact angle
Contact angle
The contact angle is the angle at which a liquid/vapor interface meets a solid surface. The contact angle is specific for any given system and is determined by the interactions across the three interfaces. Most often the concept is illustrated with a small liquid droplet resting on a flat...

 formed between a liquid and solid phase will exhibit a range of contact angles that are possible. There are two common methods for measuring this range of contact angles. The first method is referred to as the tilting base method. Once a drop is dispensed on the surface with the surface level, the surface is then tilted from 0° to 90°. As the drop is tilted, the downhill side will be in a state of imminent wetting while the uphill side will be in a state of imminent dewetting. As the tilt increases the downhill contact angle will increase and represents the advancing contact angle while the uphill side will decrease; this is the receding contact angle. The values for these angles just prior to the drop releasing will typically represent the advancing and receding contact angles. The difference between these two angles is the contact angle hysteresis. The second method is often referred to as the add/remove volume method. When the maximum liquid volume is removed from the drop without the interfacial area decreasing the receding contact angle is thus measured. When volume is added to the maximum before the interfacial area increases, this is the advancing contact angle. As with the tilt method, the difference between the advancing and receding contact angles is the contact angle hysteresis. Most researchers prefer the tilt method; the add/remove method requires that a tip or needle stay embedded in the drop which can affect the accuracy of the values, especially the receding contact angle.

Adsorption hysteresis

Hysteresis can also occur during physical adsorption
Adsorption is the adhesion of atoms, ions, biomolecules or molecules of gas, liquid, or dissolved solids to a surface. This process creates a film of the adsorbate on the surface of the adsorbent. It differs from absorption, in which a fluid permeates or is dissolved by a liquid or solid...

 processes. In this type of hysteresis, the quantity adsorbed is different when gas is being added than it is when being removed. The specific causes of adsorption hysteresis are still an active area of research, but it is linked to differences in the nucleation and evaporation mechanisms inside mesopores. These mechanisms are further complicated by effects such as cavitation
Cavitation is the formation and then immediate implosion of cavities in a liquidi.e. small liquid-free zones that are the consequence of forces acting upon the liquid...

 and pore blocking.

In physical adsorption, hysteresis is evidence of mesoporosity-indeed, the definition of mesopores (2–50 nm) is associated with the appearance (50 nm) and disappearance (2 nm) of mesoporosity in nitrogen adsorption isotherms as a function of Kelvin radius. An adsorption isotherm showing hysteresis is said to be of Type IV (for a wetting adsorbate) or Type V (for a non-wetting adsorbate), and hysteresis loops themselves are classified according to how symmetric the loop is. Adsorption hysteresis loops also have the unusual property that it is possible to scan within a hysteresis loop by reversing the direction of adsorption while on a point on the loop. The resulting scans are called "crossing," "converging," or "returning," depending on the shape of the isotherm at this point.

Matric potential hysteresis

The relationship between matric water potential
Water potential
Water potential is the potential energy of water per unit volume relative to pure water in reference conditions. Water potential quantifies the tendency of water to move from one area to another due to osmosis, gravity, mechanical pressure, or matrix effects such as surface tension...

 and water content
Water content
Water content or moisture content is the quantity of water contained in a material, such as soil , rock, ceramics, fruit, or wood. Water content is used in a wide range of scientific and technical areas, and is expressed as a ratio, which can range from 0 to the value of the materials' porosity at...

 is the basis of the water retention curve
Water retention curve
Water retention curve is the relationship between the water content, θ, and the soil water potential, ψ. This curve is characteristic for different types of soil, and is also called the soil moisture characteristic....

. Matric potential measurements (Ψm) are converted to volumetric water content (θ) measurements based on a site or soil specific calibration curve. Hysteresis is a source of water content measurement error. Matric potential hysteresis arises from differences in wetting behaviour causing dry medium to re-wet; that is, it depends on the saturation history of the porous medium. Hysteretic behaviour means that, for example, at a matric potential (Ψm) of , the volumetric water content (θ) of a fine sandy soil matrix could be anything between 8% to 25%.

A Tensiometer as it applies to physics is an instrument used to measure the surface tension of liquids.-Goniometer/Tensiometer:...

s are directly influenced by this type of hysteresis. Two other types of sensors used to measure soil water matric potential are also influenced by hysteresis effects within the sensor itself. Resistance blocks, both nylon and gypsum based, measure matric potential as a function of electrical resistance. The relation between the sensor’s electrical resistance and sensor matric potential is hysteretic. Thermocouples measure matric potential as a function of heat dissipation. Hysteresis occurs because measured heat dissipation depends on sensor water content, and the sensor water content–matric potential relationship is hysteretic. , only desorption curves are usually measured during calibration of soil moisture sensors
Soil moisture sensors
Soil moisture sensors measure the water content in soil. A soil moisture probe is made up of multiple soil moisture sensors. One common type of soil moisture sensors in commercial use is a Frequency domain sensor such as a capacitance sensor...

. Despite the fact that it can be a source of significant error, the sensor specific effect of hysteresis is generally ignored.

Magnetic hysteresis

When an external magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

 is applied to a ferromagnet
Ferromagnetism is the basic mechanism by which certain materials form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished...

 such as iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...

, the atomic dipole
In physics, there are several kinds of dipoles:*An electric dipole is a separation of positive and negative charges. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some distance. A permanent electric dipole is called an electret.*A...

s align themselves with it. Even when the field is removed, part of the alignment will be retained: the material has become magnetized. Once magnetized, the magnet will stay magnetized indefinitely. To demagnetize it requires heat or a magnetic field in the opposite direction. This is the effect that provides the element of memory in a hard disk drive.

The relationship between field strength and magnetization is not linear in such materials. If a magnet is demagnetized and the relationship between and is plotted for increasing levels of field strength, follows the initial magnetization curve. This curve increases rapidly at first and then approaches an asymptote
In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. Some sources include the requirement that the curve may not cross the line infinitely often, but this is unusual for modern authors...

 called magnetic saturation
Saturation (magnetic)
Seen in some magnetic materials, saturation is the state reached when an increase in applied external magnetizing field H cannot increase the magnetization of the material further, so the total magnetic field B levels off...

. If the magnetic field is now reduced monotonically, follows a different curve. At zero field strength, the magnetization is offset from the origin by an amount called the remanence
Remanence or remanent magnetization is the magnetization left behind in a ferromagnetic material after an external magnetic field is removed. It is also the measure of that magnetization. Colloquially, when a magnet is "magnetized" it has remanence...

. If the relationship is plotted for all strengths of applied magnetic field the result is a hysteresis loop called the main loop. The width of the middle section is twice the coercivity
In materials science, the coercivity, also called the coercive field or coercive force, of a ferromagnetic material is the intensity of the applied magnetic field required to reduce the magnetization of that material to zero after the magnetization of the sample has been driven to saturation...

 of the material.

A closer look at a magnetization curve generally reveals a series of small, random jumps in magnetization called Barkhausen jumps
Barkhausen effect
The Barkhausen effect is a name given to the noise in the magnetic output of a ferromagnet when the magnetizing force applied to it is changed...

. This effect is due to crystallographic defect
Crystallographic defect
Crystalline solids exhibit a periodic crystal structure. The positions of atoms or molecules occur on repeating fixed distances, determined by the unit cell parameters. However, the arrangement of atom or molecules in most crystalline materials is not perfect...

s such as dislocation
In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials...


Physical origin

The phenomenon of hysteresis in ferromagnetic
Ferromagnetism is the basic mechanism by which certain materials form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished...

 materials is the result of two effects: rotation of magnetization
In classical electromagnetism, magnetization or magnetic polarization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material...

 and changes in size or number of magnetic domains. In general, the magnetization varies (in direction but not magnitude) across a magnet, but in sufficiently small magnets, it does not. In these single-domain
Single domain (magnetic)
Single domain, in magnetism, refers to the state of a ferromagnet in which the magnetization does not vary across the magnet. A magnetic particle that stays in a single domain state for all magnetic fields is called a single domain particle . Such particles are very small...

 magnets, and the magnetization responds to a magnetic field by rotating. Single-domain magnets are used wherever a strong, stable magnetization is needed (for example, magnetic recording).

Larger magnets are divided into regions called domains. Across each domain, the magnetization does not vary; but between domains are relatively thin domain walls in which the direction of magnetization rotates from the direction of one domain to another. If the magnetic field changes, the walls move, changing the relative sizes of the domains. Because the domains are not magnetized in the same direction, the magnetic moment
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...

 per unit volume is smaller than it would be in a single-domain magnet; but domain walls involve rotation of only a small part of the magnetization, so it is much easier to change the magnetic moment. The magnetization can also change by addition or subtraction of domains (called nucleation and denucleation).

Magnetic hysteresis models

The most known empirical models in hysteresis are Preisach
Preisach model of hysteresis
The Preisach model of hysteresis generalizes hysteresis loops as the parallel connection of independent relay hysterons. It was first suggested in 1935 by Ferenc Preisach in the German academic journal "Zeitschrift für Physik". Since then, it has become a widely accepted model of hysteresis...

 and Jiles-Atherton models. These models allow an accurate modeling of the hysteresis loop and are widely used in the industry. However, these models lose the connection with thermodynamics and the energy consistency is not ensured. Last models rely on a consistent thermodynamic formulation. VINCH model is inspired by the kinematic hardening
Work hardening
Work hardening, also known as strain hardening or cold working, is the strengthening of a metal by plastic deformation. This strengthening occurs because of dislocation movements within the crystal structure of the material. Any material with a reasonably high melting point such as metals and...

 laws and by the thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

 of irreversible processes. In particular, in addition to provide an accurate modeling, the stored magnetic energy and the dissipated energy are known at all times. The obtained incremental formulation is variationally consistent, i.e., all internal variables follow from the minimization of a thermodynamic potential. That allows to obtain easily a vectorial model while Preisach and Jiles-Atherton are fundamentally scalar models.


There are a great variety of applications of the hysteresis in ferromagnets. Many of these make use of their ability to retain a memory, for example magnetic tape
Magnetic tape
Magnetic tape is a medium for magnetic recording, made of a thin magnetizable coating on a long, narrow strip of plastic. It was developed in Germany, based on magnetic wire recording. Devices that record and play back audio and video using magnetic tape are tape recorders and video tape recorders...

, hard disks, and credit card
Credit card
A credit card is a small plastic card issued to users as a system of payment. It allows its holder to buy goods and services based on the holder's promise to pay for these goods and services...

s. In these applications, hard magnets (high coercivity) like iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...

 are desirable so the memory is not easily erased.

Soft magnets (low coercivity) are used as cores in electromagnet
An electromagnet is a type of magnet in which the magnetic field is produced by the flow of electric current. The magnetic field disappears when the current is turned off...

s. The nonlinear response of the magnetic moment to a magnetic field boosts the response of the coil wrapped around it. The low coercivity reduces that energy loss associated with hysteresis.

Electrical hysteresis

Electrical hysteresis typically occurs in ferroelectric material, where domains of polarization contribute to the total polarization. Polarization is the electrical dipole moment (either C·m
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

−2 or C·m
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

). The mechanism, an organization of the polarization into domains, is similar to that of magnetic hysteresis.

Liquid–solid-phase transitions

Hysteresis manifests itself in state transitions when melting temperature
Melting temperature
Melting temperature may refer to:* Melting point, the temperature at which a substance changes from solid to liquid state.* DNA melting temperature, the temperature at which a DNA double helix dissociates into single strands....

 and freezing temperature do not agree. For example, agar
Agar or agar-agar is a gelatinous substance derived from a polysaccharide that accumulates in the cell walls of agarophyte red algae. Throughout history into modern times, agar has been chiefly used as an ingredient in desserts throughout Asia and also as a solid substrate to contain culture medium...

 melts at 85 °C
Celsius is a scale and unit of measurement for temperature. It is named after the Swedish astronomer Anders Celsius , who developed a similar temperature scale two years before his death...

 and solidifies from 32 to 40 °C. This is to say that once agar is melted at 85 °C, it retains a liquid state until cooled to 40 °C. Therefore, from the temperatures of 40 to 85 °C, agar can be either solid or liquid, depending on which state it was before.

Cell biology and genetics

Cells undergoing cell division
Cell division
Cell division is the process by which a parent cell divides into two or more daughter cells . Cell division is usually a small segment of a larger cell cycle. This type of cell division in eukaryotes is known as mitosis, and leaves the daughter cell capable of dividing again. The corresponding sort...

 exhibit hysteresis in that it takes a higher concentration of cyclin
Cyclins are a family of proteins that control the progression of cells through the cell cycle by activating cyclin-dependent kinase enzymes.- Function :...

s to switch them from G2 phase into mitosis
Mitosis is the process by which a eukaryotic cell separates the chromosomes in its cell nucleus into two identical sets, in two separate nuclei. It is generally followed immediately by cytokinesis, which divides the nuclei, cytoplasm, organelles and cell membrane into two cells containing roughly...

 than to stay in mitosis once begun.
Darlington in his classic works on genetics
Genetics , a discipline of biology, is the science of genes, heredity, and variation in living organisms....

 discussed hysteresis of the chromosomes, by which he meant "failure of the external form of the chromosomes to respond immediately to the internal stresses due to changes in their molecular spiral", as they lie in a somewhat rigid medium in the limited space of the cell nucleus
Cell nucleus
In cell biology, the nucleus is a membrane-enclosed organelle found in eukaryotic cells. It contains most of the cell's genetic material, organized as multiple long linear DNA molecules in complex with a large variety of proteins, such as histones, to form chromosomes. The genes within these...

In developmental biology
Developmental biology
Developmental biology is the study of the process by which organisms grow and develop. Modern developmental biology studies the genetic control of cell growth, differentiation and "morphogenesis", which is the process that gives rise to tissues, organs and anatomy.- Related fields of study...

, cell type diversity is regulated by long range-acting signaling molecules called morphogens that pattern uniform pools of cells in a concentration- and time-dependent manner. The morphogen Sonic Hedgehog
Sonic hedgehog
Sonic hedgehog homolog is one of three proteins in the mammalian signaling pathway family called hedgehog, the others being desert hedgehog and Indian hedgehog . SHH is the best studied ligand of the hedgehog signaling pathway. It plays a key role in regulating vertebrate organogenesis, such as...

 (Shh), for example, acts on limb bud
Limb bud
In embryology, the limb bud is a structure formed by the developing limb, derived from lateral plate mesoderm. It is intimately related with the apical ectodermal ridge, which secretes factors inducing the initial differentiation of the limb bud...

 and neural progenitors to induce expression of a set of homeodomain-containing transcription factors to subdivide these tissues into distinct domains. It has been shown that these tissues have a 'memory' of previous exposure to Shh.
In neural tissue, this hysteresis is regulated by a homeodomain (HD) feedback circuit that amplifies Shh signaling. In this circuit, expression of Gli
GLI may refer to:* The Volkswagen GLI, a high performance version of the Volkswagen Jetta* Great Lakes Initiative, the fictional Marvel Comics superteam formerly known as the Great Lakes Avengers...

 transcription factors, the executors of the Shh pathway, is suppressed. Glis are processed to repressor forms (GliR) in the absence of Shh, but in the presence of Shh, a proportion of Glis are maintained as full-length proteins allowed to translocate to the nucleus, where they act as activators (GliA) of transcription. By reducing Gli expression then, the HD transcription factors reduce the total amount of Gli (GliT), so a higher proportion of GliT can be stabilized as GliA for the same concentration of Shh.


There is some evidence that T cells exhibit hysteresis in that it takes a lower signal threshold to activate T cells that have been previously activated. Ras activation is required for downstream effector functions of activated T cells . Triggering of the T cell receptor induces high levels of Ras activation, which results in higher levels of GTP-bound (active) Ras at the cell surface. Since higher levels of active Ras have accumulated at the cell surface in T cells that have been previously stimulated by strong engagement of the T cell receptor, weaker subsequent T cell receptor signals received shortly afterwards will deliver the same level of activation due to the presence of higher levels of already activated Ras as compared to a naïve cell.


The property by which some neuron
A neuron is an electrically excitable cell that processes and transmits information by electrical and chemical signaling. Chemical signaling occurs via synapses, specialized connections with other cells. Neurons connect to each other to form networks. Neurons are the core components of the nervous...

s do not return to their basal conditions from a stimulated condition immediately after removal of the stimulus is an example of hysteresis.

Respiratory physiology

Lung hysteresis is evident when observing the compliance of a lung on inspiration versus expiration. The difference in compliance (volume/pressure) is due to the additional energy required during inspiration to recruit and inflate additional alveoli.

The transpulmonary pressure
Transpulmonary pressure
Transpulmonary pressure is a term used to describe the difference between the alveolar pressure and the intrapleural pressure in the lungs. During human ventilation, air flows because of pressure gradients.Ptp = Palv - Pip...

 vs Volume curve of inhalation is different from the Pressure vs Volume curve of exhalation, the difference being described as hysteresis. Lung volume at any given pressure during inhalation is less than the lung volume at any given pressure during exhalation.

Hysteresis in economics

Economic systems can exhibit hysteresis. For example, export
The term export is derived from the conceptual meaning as to ship the goods and services out of the port of a country. The seller of such goods and services is referred to as an "exporter" who is based in the country of export whereas the overseas based buyer is referred to as an "importer"...

 performance is subject to strong hysteresis effects: because of the fixed transportation costs it may take a big push to start a country's exports, but once the transition is made, not much may be required to keep them going.

Hysteresis is used extensively in the area of labor markets. According to theories based on hysteresis, economic downturns (recession) result in an individual becoming unemployed, losing his/her skills (commonly developed 'on the job'), demotivated/disillusioned, and employers may use time spent in unemployment as a screen. In times of an economic upturn or 'boom', the workers affected will not share in the prosperity, remaining long-term unemployed (over 52 weeks). Hysteresis has been put forward as a possible explanation for the poor unemployment performance of many economies in the 1990s. Labor market reform, and/or strong economic growth, may not therefore aid this pool of long-term unemployed, and thus specific targeted training programs are presented as a possible policy solution.

Permanently higher unemployment

Hysteresis is a hypothesized property of unemployment rates. It's possible that there is a ratchet effect
Ratchet effect
A metaphorical ratchet effect is an instance of the restrained ability of human processes to be reversed once a specific thing has happened, analogous with the mechanical ratchet that holds the spring tight as a clock is wound up...

, so a short-term rise in unemployment rates tends to persist.

An example is the notion that inflationary policy leads to a permanently higher 'natural' rate of unemployment (NAIRU
In monetarist economics, particularly the work of Milton Friedman, on which also worked Lucas Papademos and Franco Modigliani in 1975,NAIRU is an acronym for Non-Accelerating Inflation Rate of Unemployment, and refers to a level of unemployment below which inflation rises.It is widely used in...

), because inflationary expectations are 'sticky
Sticky (economics)
Sticky, in the social sciences and particularly economics, describes a situation in which a variable is resistant to change. Sticky prices are an important part of macroeconomic theory since they may be used to explain why markets might not reach equilibrium right away. Nominal wages are often said...

' downward due to wage rigidities and imperfections in the labour market.

When some negative shock reduces employment in a company or industry, there are fewer employed workers left. As usually the employed workers have the power to set wages, their reduced number incentivizes them to bargain for even higher wages when the economy again gets better, instead of letting the wage be at the equilibrium wage
Equilibrium wage
In economics, the equilibrium wage is the wage rate that produces neither an excess supply of workers nor an excess demand for workers and labor market. See economic equilibrium....

 level, where the supply and demand of workers would match. This causes hysteresis, i.e., the unemployment becomes permanently higher after negative shocks.

Another channel through which hysteresis can occur is through learning by doing. Workers who lose their jobs due to a temporary shock may become permanently unemployed because they miss out on the job training and skill acquisition that normally takes place.

Hysteresis has been invoked, by Olivier Blanchard
Olivier Blanchard
Olivier Jean Blanchard is currently the chief economist at the International Monetary Fund, a post he has held since September 1, 2008. He is also the Class of 1941 Professor of Economics at MIT, though he is currently on leave. Blanchard is one of the most cited economists in the world, according...

 among others, as explaining the differences in long run unemployment rates between Europe and the United States.

Game theory and capital controls

Hysteresis occurs in applications of game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...

 to economics, in models with product quality, agent honesty or corruption of various institutions. Slightly different initial conditions can lead to opposite outcomes and resulting stable "good" and "bad" equilibria
Correlated equilibrium
In game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. It was first discussed by mathematician Robert Aumann . The idea is that each player chooses his/her action according to his/her observation of the value of the same public...


Another area where hysteresis phenomena are found is capital controls. A developing country can ban a certain kind of capital flow (e.g. engagement with international private equity funds), but when the ban is removed, the system takes a long time to return to the pre-ban state.

Models of hysteresis

Each subject that involves hysteresis has models that are specific to the subject. In addition, there are models that capture general features of many systems with hysteresis. An example is the Preisach model of hysteresis
Preisach model of hysteresis
The Preisach model of hysteresis generalizes hysteresis loops as the parallel connection of independent relay hysterons. It was first suggested in 1935 by Ferenc Preisach in the German academic journal "Zeitschrift für Physik". Since then, it has become a widely accepted model of hysteresis...

, which represents a hysteresis nonlinearity as a superposition of square loops called hysterons.

A simple parametric description of various hysteretic loops may be found in the Lapshin model of hysteresis. Along with the classical loop (see example in Fig. 1), substitution of rectangle, triangle or trapezoidal pulses instead of the harmonic functions also allows piecewise-linear hysteresis loops frequently used in discrete automatics to be built in the model (see example in Fig. 4).

The Bouc-Wen model of hysteresis
Bouc-Wen model of hysteresis
The Bouc-Wen model is a model that is often used to describe non-linear hysteretic systems. It was introduced by Bouc and extended by Wen , who demonstrated its versatibility by producing a variety of hysteretic patterns....

 is often used to describe non-linear hysteretic systems. It was introduced by Bouc and extended by Wen, who demonstrated its versatility by producing a variety of hysteretic patterns. This model is able to capture in analytical form, a range of shapes of hysteretic cycles which match the behaviour of a wide class of hysteretical systems; therefore, given its versability and mathematical tractability, the Bouc-Wen model has quickly gained popularity and has been extended and applied to a wide variety of engineering problems, including multi-degree-of-freedom (MDOF) systems, buildings, frames, bidirectional and torsional
Torsion (mechanics)
In solid mechanics, torsion is the twisting of an object due to an applied torque. In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius....

 response of hysteretic systems two- and three-dimensional continua, and soil liquefaction
Soil liquefaction
Soil liquefaction describes a phenomenon whereby a saturated soil substantially loses strength and stiffness in response to an applied stress, usually earthquake shaking or other sudden change in stress condition, causing it to behave like a liquid....

 among others. The Bouc-Wen model and its variants/extensions have been used in applications of structural control
Structural engineering
Structural engineering is a field of engineering dealing with the analysis and design of structures that support or resist loads. Structural engineering is usually considered a specialty within civil engineering, but it can also be studied in its own right....

, in particular in the modeling of the behaviour of magnetorheological dampers, base isolation
Base isolation
Base isolation, also known as seismic base isolation or base isolation system, is one of the most popular means of protecting a structure against earthquake forces...

 devices for buildings and other kinds of damping devices; it has also been in the modelling and analysis of structures built of reinforced concrete, steel, mansory and timber.


When hysteresis occurs with extensive and intensive variable
Intensive and extensive properties
In the physical sciences, an intensive property , is a physical property of a system that does not depend on the system size or the amount of material in the system: it is scale invariant.By contrast, an extensive property In the physical sciences, an intensive property (also called a bulk...

s, the work done on the system is the area under the hysteresis graph.

See also

  • Hysteresivity
    Hysteresivity derives from “hysteresis”, meaning “lag”. It is the tendency to react slowly to an outside force, or to not return completely to its original state...

  • Path dependence
    Path dependence
    Path dependence explains how the set of decisions one faces for any given circumstance is limited by the decisions one has made in the past, even though past circumstances may no longer be relevant....

  • Backlash (engineering)
    Backlash (engineering)
    In mechanical engineering, backlash, sometimes called lash or play, is clearance between mating components, sometimes described as the amount of lost motion due to clearance or slackness when movement is reversed and contact is re-established...

  • Bean's critical state model
    Bean's critical state model
    Bean's critical state model, introduced by C. P. Bean in 1962, gives a macroscopic explanation of the irreversible magnetization behavior of hard Type-II superconductors.-Assumptions:...

External links

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