![]() ![]() We call such automata \(\ell \)AQS-A and work out the structure of their state transition graphs. This enables us to consider AQS-A exhibiting RPM without necessarily possessing the no-passing property. We show that the AQS dynamics provides a more selective partial order which, due to its explicit connection to hysteresis loops, is a natural choice for establishing the RPM property. While sufficient, conditions (1)–(3) are not necessary. When periodically driven, such systems settle into a cyclic response after a transient of at most one period. The existence of three conditions, (1) a partial order on the set of configuration (2) a no-passing property and (3) an adiabatic response to monotonously changing fields, implies RPM. Our interest is in an automaton description (AQS-A) that represents the AQS dynamics via a graph of state transitions triggered by the field and in the presence of return-point-memory (RPM) property, a tendency for the system to return to the same microstate upon cycling driving. We consider the athermal quasi-static dynamics (AQS) of disordered systems driven by an external field. ![]()
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