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.