  The event-chain Monte Carlo (ECMC) method is an irreversible Markov process
based on the factorized Metropolis filter and the concept of lifted Markov
chains. Here, ECMC is applied to all-atom models of multi-particle interactions
that include the long-ranged Coulomb potential. We discuss a line-charge model
for the Coulomb potential and demonstrate its equivalence with the standard
Coulomb model with tin-foil boundary conditions. Efficient factorization
schemes for the potentials used in all-atom water models are presented, before
we discuss the best choice for lifting schemes for factors of more than three
particles. The factorization and lifting schemes are then applied to
simulations of point-charge and charged-dipole Coulomb gases, as well as to
small systems of liquid water. For a locally charge-neutral system in three
dimensions, the algorithmic complexity is O(N log N) in the number N of
particles. In ECMC, a Particle-Particle method, it is achieved without the
interpolating mesh required for the efficient implementation of other modern
Coulomb algorithms. An event-driven, cell-veto-based implementation samples the
equilibrium Boltzmann distribution using neither time-step approximations nor
spatial cutoffs on the range of the interaction potentials. We discuss
prospects and challenges for ECMC in soft condensed-matter and biological
physics.
