  A new Markov Chain Monte Carlo method for simulating the dynamics of
molecular systems characterized by hard-core interactions is introduced. In
contrast to traditional Kinetic Monte Carlo approaches, where the state of the
system is associated with minima in the energy landscape, in the proposed
method, the state of the system is associated with the set of paths traveled by
the atoms and the transition probabilities for an atom to be displaced are
proportional to the corresponding velocities. In this way, the number of
possible state-to-state transitions is reduced to a discrete set, and a direct
link between the Monte Carlo time step and true physical time is naturally
established. The resulting rejection-free algorithm is validated against
event-driven molecular dynamics: the equilibrium and non-equilibrium dynamics
of hard disks converge to the exact results with decreasing displacement size.
