Often thermodynamical phenomena are described microscopically by a randomly evolving particle system, or macroscopically by an evolution equation, and the two levels of descrip- tion are connected by sending the number of particles to infinity. Onsager and Machlup pos- tulated that microscopic systems in detailed balance (reversible Markov process) behave as a gradient flow on the macroscopic level. This principle is now well-understood and can be made precise via the theory of large deviations. In order to understand the behaviour of non-equilibrium systems (not in detailed balance/nonreversible), one commonly studies par- ticle densities as well as particle fluxes; this is the topic of Macroscopic Fluctuation Theory. Classically the large deviations yield a natural Hilbert structure that allows to decompose the dynamics into a gradient flow component (dissipating free energy) and a Hamiltonian com- ponent (conserving energy). For systems where the particles hop between discrete sites, and the macroscopic equation is a system of ODEs, such natural Hilbert space is not available. We present a generalised Macroscopic Fluctuation Theory, sufficiently general to apply to, for example zero-range processes and chemical reactions. This work lies on the boundary between probability, analysis and physics, but I will mostly fo- cus on the analysis and physics part.