  We have created a functional framework for a class of non-metric gradient
systems. The state space is a space of nonnegative measures, and the class of
systems includes the Forward Kolmogorov equations for the laws of Markov jump
processes on Polish spaces. This framework comprises a definition of a notion
of solutions, a method to prove existence, and an archetype uniqueness result.
We do this by using only the structure that is provided directly by the
dissipation functional, which need not be homogeneous, and we do not appeal to
any metric structure.
