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In one-dimensional random walks, the waiting time for each directiontransitions is the same, even in the presence of bias, as a consequence of themicroscopic-reversibility. We study the symmetry breaking of forward/ backwardtransition times in a random walk on a lattice of two lanes. We find thateither transition times can be faster depending on the lattice's net current,and the symmetry is recovered only at equilibrium. Our analysis suggests thatthe forward/ backward transition times' asymmetry can be used as a measure ofdeviation from the equilibrium of the system.

Asymmetry of forward/backward transition times as a non-equilibrium measure of complexity of microscopic mechanisms