A system with hysteresis has memory. Such a system is said to exhibit path-dependence, or "rate-independent memory". (Mielke & Roubicek 2003). In a deterministic system with no dynamics or hysteresis, it is possible to predict the system's output at an instant in time, given only its input at that instant in time. In a system with hysteresis, this is not possible; there is no way to predict the output without knowing the system's current state, and there is no way to know the system's state without looking at the history of the input. This means that it is necessary to know the path that the input followed before it reached its current value. Many physical systems naturally exhibit hysteresis. A piece of iron that is brought into a magnetic field retains some magnetization, even after the external magnetic field is removed. Once magnetized, the iron will stay magnetized indefinitely. To demagnetize the iron, it would be necessary to apply a magnetic field in the opposite direction. This is the effect that provides the element of memory in a hard disk drive. A system may be explicitly designed to exhibit hysteresis, especially in control theory

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