  Stochastic biochemical and transport processes have various final outcomes,
and they can be viewed as dynamic systems with multiple exits. Many current
theoretical studies, however, typically consider only a single time scale for
each specific outcome, effectively corresponding to a single-exit process and
assuming the independence of each exit process. But the presence of other exits
influences the statistical properties and dynamics measured at any specific
exit. Here, we present theoretical arguments to explicitly show the existence
of different time scales, such as mean exit times and inverse exit fluxes, for
dynamic processes with multiple exits. This implies that the statistics of any
specific exit dynamics cannot be considered without taking into account the
presence of other exits. Several illustrative examples are described in detail
using analytical calculations, mean-field estimates, and kinetic Monte Carlo
computer simulations. The underlying microscopic mechanisms for the existence
of different time scales are discussed. The results are relevant for
understanding the mechanisms of various biological, chemical, and industrial
processes, including transport through channels and pores.
