  We present an algorithm for the simulation of the exact real-time dynamics of
classical many-body systems with discrete energy levels. In the same spirit of
kinetic Monte Carlo methods, a stochastic solution of the master equation is
found, with no need to define any other phase-space construction. However,
unlike existing methods, the present algorithm does not assume any particular
statistical distribution to perform moves or to advance the time, and thus is a
unique tool for the numerical exploration of fast and ultra-fast dynamical
regimes. By decomposing the problem in a set of two-level subsystems, we find a
natural variable step size, that is well defined from the normalization
condition of the transition probabilities between the levels. We successfully
test the algorithm with known exact solutions for non-equilibrium dynamics and
equilibrium thermodynamical properties of Ising-spin models in one and two
dimensions, and compare to standard implementations of kinetic Monte Carlo
methods. The present algorithm is directly applicable to the study of the real
time dynamics of a large class of classical markovian chains, and particularly
to short-time situations where the exact evolution is relevant.
