In a world made of atoms, the computer simulation of molecular systems, such
as proteins in water, plays an enormous role in science. Software packages that
perform these computations have been developed for decades. In molecular
simulation, Newton's equations of motion are discretized and long-range
potentials are treated through cutoffs or spacial discretization, which all
introduce approximations and artifacts that must be controlled algorithmically.
Here, we introduce a paradigm for molecular simulation that is based on modern
concepts in statistics and is rigorously free of discretizations,
approximations, and cutoffs. Our demonstration software reaches a break-even
point with traditional molecular simulation at high precision. We stress the
promise of our paradigm as a gold standard for critical applications and as a
future competitive approach to molecular simulation.Comment: 19 pages, 4 figures; 18 pages supplementary materials, 1
supplementary figur