The structure of state transition graphs in systems with return point memory. I. General theory (Q2001967)

The authors consider the athermal quasi-static dynamics (AQS) of disordered systems driven by an external field and select automation 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. It is shown that the RPM property constrains the intra-loop structure of hysteresis loops, namely its hierarchical organization into sub-loops, but not the inter-loop structure. The authors prove that the topology of the intra-loop structure can be represented as an ordered tree and show that the corresponding state transition graph is planar. A system exhibiting RPM and subject to periodic forcing can undergo a large number of transient cycles before setting into a periodic response.