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We study the distribution of the time-integrated current in anexactly-solvable toy model of heat conduction, both analytically andnumerically. The simplicity of the model allows us to derive the full currentlarge deviation function and the system statistics during a large deviationevent. In this way we unveil a relation between system statistics at the end ofa large deviation event and for intermediate times. Midtime statistics isindependent of the sign of the current, a reflection of the time-reversalsymmetry of microscopic dynamics, while endtime statistics do depend on thecurrent sign, and also on its microscopic definition. We compare our exactresults with simulations based on the direct evaluation of large deviationfunctions, analyzing the finite-size corrections of this simulation method andderiving detailed bounds for its applicability. We also show how theGallavotti-Cohen fluctuation theorem can be used to determine the range ofvalidity of simulation results.

Current Fluctuations and Statistics During a Large Deviation Event in an Exactly-Solvable Transport Model