On the symmetry of current probability distributions in jump processes

Abstract: We study the symmetry of large deviation functions associated with time-integrated currents in Markov pure jump processes. One current known to have this symmetry is the fluctuating entropy production and this is the content of the fluctuation theorem. Here we obtain a necessary condition in order to have a current different from entropy with a symmetric large deviation function. This condition is related to degeneracies in the set of increments associated with fundamental cycles from Schnakenberg network theory. Moreover we consider 4-states systems where we explicitly show that non-entropic time-integrated currents can be symmetric. We also show that these new symmetries, as is the case of the fluctuation theorem, are related to time-reversal. However, this becomes apparent only when stochastic trajectories are appropriately grouped together.