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Hysteresis

Prime #
48
Origin domain
Physics
Also from
Economics & Finance, Biology & Ecology
Related primes
Irreversibility, Half-Life, Oscillation, Damping, Frame of Reference, State and State Transition, Tipping Points (or Phase Transitions), Feedback

Core Idea

A system's response to external forces or changes depends on its history, causing different future states under the same conditions.

How would you explain it like I'm…

The Paperclip Remembers

Bend a paperclip a little and let go; it springs back. Bend it a lot and let go; it stays bent. Where the paperclip ends up depends on what you did to it before, not just where your hand is now. The paperclip remembers.

When a System Remembers Its Past

Hysteresis is when a system's state depends on its history, not just on what's happening right now. Think of your thermostat: it turns the heater on when the room drops to 68 and off at 72, so at exactly 70 degrees it could be either on or off depending on whether the room was warming up or cooling down. The system 'remembers' the path it took to get to this point, so going back to the same temperature doesn't always undo the change.

Path-Dependent System State

Hysteresis is the property where a system's current state depends not only on the present external conditions but also on the path by which those conditions were reached. If you graph the system's response while raising and then lowering some input, you don't trace a single line; you trace a loop. A classic example is magnetizing iron: increase the magnetic field and the iron magnetizes; remove the field and it stays partly magnetized rather than returning to zero. The system has internal memory, sometimes from multiple stable states, sometimes from internal lag, sometimes from irreversible structural change.

 

Hysteresis is a property of certain dynamical systems whereby the present state depends on the history of the inputs, not merely their current value, so the response curve to a cyclically varied parameter forms a loop rather than a single-valued function. The system carries internal state (hidden from the external parameter) that encodes information about the trajectory taken. Classic examples include ferromagnetic hysteresis (iron's magnetization lags the applied field, tracing a B-H loop), elastic hysteresis (rubber's stress-strain curve differs on loading versus unloading), and economic hysteresis (unemployment persistently elevated after a recession ends, because worker skills and firm networks degrade irreversibly). Every hysteresis claim must specify the state variable being tracked, the external parameter being varied, the observed path-dependence (different states at the same parameter value), and the internal mechanism, typically one of: multiple stable equilibria, adjustment lag, or irreversible structural change.

Broad Use

  • Meteorology: Soil moisture or ice coverage may persist even if conditions revert to previous levels.

  • Biology: Memory effects in cellular processes or ecological states.

  • Economics: Unemployment rates can remain high after a recession ends (persistent joblessness).

  • Engineering: Magnetic materials retaining magnetization after an external field is removed.

Clarity

Pinpoints lag or memory effects, shedding light on why reverting external conditions may not restore a system to its original state.

Manages Complexity

Draws attention to path-dependent behaviors, preventing oversimplification of systems as purely reactive.

Abstract Reasoning

Encourages considering history and state as integral to predicting future outcomes.

Knowledge Transfer

Helps model "sticky" phenomena, from ecological baselines to post-crisis economic inertia.

Example

Sea Ice Cover: Even if temperatures return to cooler levels, ice loss may persist due to earlier melting and reduced albedo.

Relationships to Other Primes

One-hop neighborhood: parents above, mutual partners to the right, children below.Hysteresissubsumption: State and State TransitionState and StateTransitionsubsumption: Path DependencePath Dependence

Parents (2) — more general patterns this builds on

  • Hysteresis is a kind of Path Dependence — Hysteresis is a specialization of path dependence in which the loop structure is visible in the response curve to a varied parameter.
  • Hysteresis is a kind of State and State Transition — Hysteresis is a specific kind of state transition where current state depends on the path by which conditions were reached.

Path to root: Hysteresis → State and State Transition

Not to Be Confused With

  • Hysteresis is not Inertia because hysteresis is about the path-dependence of a state (returning the external parameter to a prior value does not return the state to its prior value), whereas inertia is about resistance to changes in trajectory or configuration—a system can have inertia without hysteresis, persisting in its current state when no force acts upon it.
  • Hysteresis is not Equilibrium because hysteresis describes a phenomenon of non-uniqueness and path-dependence at a given external parameter value, whereas equilibrium describes a balance condition where opposing quantities cancel—multiple equilibria can exist without hysteresis if they are path-independent.
  • Hysteresis is not Resonance because hysteresis concerns how a system's current state depends on the history of parameter changes, whereas resonance concerns how a system amplifies inputs at specific frequencies, independent of the path by which that frequency was reached.