The same reading can mean two different states

Cross-Domain EchoesShared pattern · Hysteresis

A thermometer reading alone may not tell you whether a heater is on. Between its lower turn-on temperature and upper turn-off temperature, the thermostat keeps the state reached earlier. An elementary relay in the Preisach model behaves similarly: it switches when input rises past its upper threshold or falls past its lower threshold and remembers its previous state between them. The shared idea is that present input plus history determines the state. The comparison is deliberately about this small switching rule. A full Preisach model combines many weighted relays to represent hysteresis; a thermostat also senses temperature, drives a heater and participates in a physical feedback loop.

Written comparison

Present reading

Models of magnetic materials

Scalar input, such as applied field

Heating control

Measured room temperature

Current input alone does not determine the switch state inside the band.

Falling below the lower boundary

Models of magnetic materials

Relay switches to its lower-input state

Heating control

Heater switches on

A falling input crossing the lower threshold sets this state. Re-entering the band upward through the lower threshold does not itself switch the state.

Rising above the upper boundary

Models of magnetic materials

Relay switches to its higher-input state

Heating control

Heater switches off

A rising input crossing the upper threshold sets the other state. Re-entering the band downward through the upper threshold does not itself switch the state.

Between the boundaries

Models of magnetic materials

Relay retains its previous state

Heating control

Heater continues its current on/off state

Inside the band, the last state-setting crossing determines the retained state. Two histories can reach the same reading with different states; a crossing in the non-switching direction does not reset it.

What carries across

When state depends on history, record the last transition as well as the current reading. A single cutoff cannot describe a two-threshold rule.

Where the comparison stops

The shared rule belongs to one elementary relay and the thermostat switch. Weighted aggregation, material behavior and the room’s physical heating dynamics do not map across.

• The full Preisach model is a weighted superposition, not one relay and not a thermostat. The comparison maps its elementary memory rule only.
• The classical Preisach operator is rate-independent. A real room and heater have physical timing; that rate-independence claim does not transfer to the heating system.
• A thermostat’s band is intentionally chosen to reduce chattering. A fitted material model describes observed hysteresis; fitting relays does not prove literal binary material components or an engineering purpose.

Conditions for this comparison

• The left illustration shows one elementary relay inside a full weighted Preisach model.
• Only rising past the upper or falling past the lower threshold sets the corresponding state.
• The thermostat has distinct heating-on and heating-off temperatures; physical room dynamics are not a rate-independent operator.

Source entries

Shared pattern

Hysteresis

Prime

Core Idea

history is encoded in the system's internal state in a way that the external parameter alone cannot reveal

Models of magnetic materials

Preisach model of hysteresis

Domain-specific abstraction

Core Idea

Each relay switches into one state when the scalar input crosses an upper threshold and into the other when the input crosses a lower threshold. Between thresholds it retains its previous state, so present output depends on input history rather than current input alone.

Structural Signature

A single present input value is insufficient to determine output.

What It Is Not

It is not one Schmitt trigger or relay; the distributed weighted superposition is constitutive.

Heating control

Thermostat Control

Mechanism

Example

When a cold front drops the reading to 20.4 °C, the comparator finds the temperature below the band and closes a relay; the furnace fires. Warm air raises the reading, and when it passes 21.5 °C the comparator opens the relay and the furnace stops. The house then coasts, cooling slowly, until the lower edge is reached again and the cycle repeats.

How it works

A small hysteresis gap between the switch-on and switch-off temperatures keeps the relay from chattering the instant the reading wobbles around a single value.