  Microscopic mechanisms of natural processes are frequently understood in
terms of random walk models by analyzing local particle transitions. This is
because these models properly account for dynamic processes at the molecular
level and provide a clear physical picture. Recent theoretical studies made a
surprising discovery that in complex systems the symmetry of molecular
forward/backward transition times with respect to local bias in the dynamics
may be broken and it may take longer to go downhill than uphill. The physical
origins of these phenomena remain not fully understood. Here we explore in more
detail the microscopic features of the symmetry breaking in the
forward/backward transition times by analyzing exactly solvable discrete-state
stochastic models. In particular, we consider a specific case of two random
walkers on four-sites periodic lattice as the way to represent the general
systems with multiple pathways. It is found that the asymmetry in transition
times depends on several factors that include the degree of deviation from
equilibrium, the particle crowding and methods of measurements of dynamic
properties. Our theoretical analysis suggests that the asymmetry in transition
times can be explored experimentally for determining the important microscopic
features of natural processes by quantitative measuring the local deviations
from equilibrium and the degrees of crowding.
