Fluctuation theorems and large-deviation functions in systems not featuring a steady state

Motivated by the time behavior of the functional arising in the variational approach to the KPZ equation, we have adapted a path-integral scheme to deal with unstable systems. We start analyzing simple toy systems, without stationary probability distribution, in order to show how to proceed for obtaining detailed as well as integral fluctuation theorems in such a kind of systems. The path integral approach adequately fits to this kind of study. This methodology, together with the variational approach, are also exploited to analyze fluctuation theorems in the paradigmatic KPZ equation, as well as to determine an entropy production Large Deviation Function. Those results lead us to conjecture that a higher critical dimension does not exist for the KPZ system.