  We propose a new route to accelerate molecular dynamics through the use of
velocity jump processes allowing for an adaptive time-step specific to each
atom-atom pair (2-body) interactions. We start by introducing the formalism of
the new velocity jump molecular dynamics, ergodic with respect to the canonical
measure. We then introduce the new BOUNCE integrator that allows for long-range
forces to be evaluated at random and optimal time-steps, leading to strong
savings in direct space. The accuracy and computational performances of a first
BOUNCE implementation dedicated to classical (non-polarizable) force fields is
tested in the cases of pure direct-space droplet-like simulations and of
periodic boundary conditions (PBC) simulations using Smooth Particule Mesh
Ewald. An analysis of the capability of BOUNCE to reproduce several condensed
phase properties is provided. Since electrostatics and van der Waals 2-body
contributions are evaluated much less often than with standard integrators
using a 1fs timestep, up to a 400 % direct-space acceleration is observed.
Applying the reversible reference system propagator algorithms (RESPA(1)) to
reciprocal space (many-body) interactions allows BOUNCE-RESPA(1) to maintain
large speedups in PBC while maintaining precision. Overall, we show that
replacing the BAOAB integrator by the BOUNCE adaptive framework preserves a
similar accuracy and leads to significant computational savings.
