Markov-chain sampling for long-range systems without evaluating the energy.

In past decades, enormous effort has been expended to develop algorithms and even to construct special-purpose computers in order to efficiently evaluate total energies and forces for long-range-interacting particle systems, with the particle-mesh Ewald and the fast multipole methods as well as the "Anton" series of supercomputers serving as examples for biomolecular simulations. Cutoffs in the range of the interaction have also been used for large systems. All these methods require extrapolations.