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In short, hysteresis is the lagging of an effect behind its cause.
A property of a system such that an output value is not a strict function of the corresponding input, but also incorporates some lag, delay, or history dependence, and in particular when the response for a decrease in the input variable is different from the response for an increase. For example, a thermostat with a nominal setpoint of 75° might switch the controlled heat source on when the temperature drops below 74°, and off when it rises above 76°.