An algorithm for parallelization of molecular dynamics in time

Non-linear, time-dependent systems typically are solved using discrete time-stepping strategies, e.g. by simulation. Parallelization schemes for such methods focus on the system or the discretization method (e.g., parallelizing force calculations in space), but are limited by the essentially sequential order of time: The solution at later times can only be computed once the solution at early times is known. Here, we present an alternate formulation of the simulation problem, suggesting a new algorithm that is parallelizable in time. The derivation and examples are presented in the context of molecular dynamics, and we describe a parallelization scheme that gives arbitrarily large speedups for sufficiently small time steps.