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