  We explore a macroscopic, algebraic approach to rate independent hysteresis
using semigroup theory. A macroscopic description of metastable states relevant
to rate independent hysteresis is introduced using field history. The semigroup
structure of the history space is identified. Using semigroup theory and
related mathematical techniques, the general relation between return point
memory (RPM) and partial order is discovered. For hysteresis system with RPM, a
variational principle is identified. The erasing properties of field histories
are also characterized. The connection between this semigroup approach and
other models are also discussed.
