hysteresis

A system with hysteresis can be summarized as a system that may be in any number of states, independent of the inputs to the system. To be exact, a system with hysteresis exhibits path-dependence, or "rate-independent memory". By contrast, consider a deterministic system with classical dynamics but no hysteresis. In that case, one 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; one cannot predict the output without looking at the history of the input, i.e., the state of the system for a given input. In order to predict the output, one must look at the path that the output 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 effect is exploited commercially; for example, it provides the element of memory in a hard disk drive.