There are many open questions surrounding the statistical mechanical characterisation of systems out of equilibrium, particularly regarding their relaxation towards equilibrium or non-equilibrium steady states, as well as the fluctuations which occur throughout their dynamics. The dissipation function of Evans and Searles [48] has found successful applications in both of these areas. In this work we investigate the use of the dissipation function to characterise these behaviours, in a number of dynamical systems. In a system which allows us to tune the chaoticity of its dynamics, we utilise the dissipation function to study the necessary conditions for fluctuation relations to be observed. This section of work teases apart the conditions of chaotic dynamics and transient mixing (T-mixing) [49, 116], showing that fluctuation relations hold in non-chaotic systems, counter to the contemporary theories of the necessary conditions. Our results suggest that the Evans-Searles Fluctuation Theorem [44, 45] may provide a more fruitful path forward for the study of fluctuations in dynamical systems. [...]