  We discuss a canonical structure that provides a unifying description of
dynamical large deviations for irreversible finite state Markov chains
(continuous time), Onsager theory, and Macroscopic Fluctuation Theory. For
Markov chains, this theory involves a non-linear relation between probability
currents and their conjugate forces. Within this framework, we show how the
forces can be split into two components, which are orthogonal to each other, in
a generalised sense. This splitting allows a decomposition of the pathwise rate
function into three terms, which have physical interpretations in terms of
dissipation and convergence to equilibrium. Similar decompositions hold for
rate functions at level 2 and level 2.5. These results clarify how bounds on
entropy production and fluctuation theorems emerge from the underlying
dynamical rules. We discuss how these results for Markov chains are related to
similar structures within Macroscopic Fluctuation Theory, which describes
hydrodynamic limits of such microscopic models.c Fluctuation Theory, which
describes hydrodynamic limits of such microscopic models.
