Limits on memory storage in amorphous solids from analysis of transition networks

We analyze the directed graph of plastic transitions obtained by shearing an initial quenched configuration. We decompose the graph into strongly connected components (SCCs) whose configurations are mutually reachable, meaning that each configuration in this component can be reached from any other configuration in the same component by a series of plastic events. We call these transitions ``reversible’' whereas transitions that connect different configurations belonging to different strongly connected components are then called ``irreversible’', since these configurations are not mutually-reachable, meaning that there is no return path. We find that the distinction between reverible and irreversible transitions also manifests itself in the microscopical properties of the underlying plastic events - irreversible transitions typically correspond to significantly larger energy drops associated with larger plastic events. We further show that the size distribution of strongly connected components follows power-law scaling and hence large SCCs are rare. Since the states of limit cycles must necessarily belong to the same SCC, this also means that large limit-cycles are rare which is consistent with previous observations.