The ergodic hypothesis states that an infinitely long trajectory of a statistical system will come arbitrarily close to any point in phase space an infinite number of times. In practical terms, this equates the long-time average of a single trajectory to the ensemble average of similarly prepared systems. It can be argued that ergodicity is a useful fiction, one that physical systems regularly violate. In many cases one can retain the canonical structure of equilibrium statistical mechanics by simply constraining Gibbsian statistics to some subset of the phase space. However, when ergodicity is broken continuously – that is, the system does not have time to sufficiently relax in each state before transitioning irreversibly to a new one – more drastic modifications to the partition function are required in frequency-space. When such violations occur, linear response breaks down and the fluctuation-dissipation theorem is violated. Such violations may be phenomenologically repaired by cranking up the kinetic temperature to some effective value, which has practical consequences on Arrhenius-type transitions such as protein electron transfer. A general expression for the non-ergodic free energy landscape can be derived and related to the equilibrium landscape by an appropriate correlation function.