Clock Monte Carlo: From computational complexity to energy extensivity

This general method allows for an efficient information extraction and a constant-time complexity by only relying on the separation of the energy into its independent components. The obtained acceleration is however limited by the disorder and frustration present in the system and we show how it is directly ruled by the energy extensivity nature, regardless of the system’s peculiarities. As previous reduction methods can be seen as special examples of this new class, this work asks the question whether the complexity of energy landscapes is a strict bound for any random walk’s complexity.