On decompositions of non-reversible processes

We consider fluxes and forces in Markov chains. In physics, the concept of so-called iso-surfaces has recently been introduced. In generic cases, there are infinitely many associated iso-dissipation forces. We first show that this is due to different notions of duality, each giving rise to dual force. We then study Hamiltonians associated to variational formulations of Markov processes, and develop different decompositions for them.