Entropy production and fluctuation relations for a KPZ interface

We study entropy production and fluctuation relations in the restricted solid-on-solid growth model, which is a microscopic realization of the Kardar-Parisi-Zhang (KPZ) equation. Solving the one-dimensional model exactly on a particular line of the phase diagram we demonstrate that entropy production quantifies the distance from equilibrium. Moreover, as an example of a physically relevant current different from the entropy, we study the symmetry of the large deviation function associated with the interface height. In a special case of a system of length L = 4 we find that the probability distribution of the variation of height has a symmetric large deviation function, displaying a symmetry different from the Gallavotti-Cohen symmetry.