A system with hysteresis exhibits path-dependence, or "rate-independent memory". By contrast, consider a deterministic system with no hysteresis and no dynamics. In that case, we can predict the output of the system at some instant in time, given only the input to the system at that instant. If the system has hysteresis, then this is not the case; we can't predict the output without looking at the history of the input. In order to predict the output, we must look at the path that the input followed before it reached its current value. A system with hysteresis has memory. 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. In order to demagnetize the iron, it would be necessary to apply a magnetic field in the opposite direction. This effect is exploited commercially;

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