  We establish a large deviation principle for the empirical measure process
associated with a general class of finite-state mean field interacting particle
systems with Lipschitz continuous transition rates that satisfy a certain
ergodicity condition. The approach is based on a variational representation for
functionals of a Poisson random measure. Under an appropriate strengthening of
the ergodicity condition, we also prove a locally uniform large deviation
principle. The main novelty is that more than one particle is allowed to change
its state simultaneously, and so a standard approach to the proof based on a
change of measure with respect to a system of independent particles is not
possible. The result is shown to be applicable to a wide range of models
arising from statistical physics, queueing systems and communication networks.
Along the way, we establish a large deviation principle for a class of jump
Markov processes on the simplex, whose rates decay to zero as they approach the
boundary of the domain. This result may be of independent interest.
