Stochastic entropies and fluctuation theorems for a generic 1D KPZ system: internal and external dynamics

In a recent numerical study, we have analyzed the stochastic entropies and fluctuation
theorems in a 1D KPZ system. Such a study only considered saturated fluctuations around the
spatial mean value of the interface. In this way stationary solutions exist and besides, with some
particular discrete version, those solutions are exactly known. In this paper we extend these
previous results in two ways. On the one hand, the dynamics of the spatial mean value is taken
into account. We then distinguish between the entropies associated with internal fluctuations (of
the interface around the spatial mean), and external fluctuations (of the spatial mean around
the sample mean) dynamics. On the other hand a broader region of parameters is analysed.
Two distinct behaviors appear depending on whether after saturation the system overcomes the
Edward-Wilkinson crossover towards the KPZ regime or not.