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. In a simple mesoscopic model and under two scenarios, we define a suitable mean value of (the exponential of) the entropy production between arbitrary initial and final states. This definition leads naturally to an integral fluctuation theorem (FT)-and on the way, to detailed and Crooks' FT. We also find the general form of a large-deviation function, as well as its particular form for a particle submitted to a constant force.