  We show that the assumptions of the detailed balance and of the initial
equilibrium macrostate, which are central to the Crooks fluctuation theorem
(CFT), lead to all microstates along a trajectory to have equilibrium
probabilities. We also point out that the Crooks's definition of the backward
trajectory does not return the system back to its initial microstate. Once
corrected, the detailed balance assumption makes the CFT a theorem only about
reversible processes involving reversible trajectories that satisfy
Kolmogorov's criterion. As there is no dissipation, the CFT cannot cover
irreversible processes, which is contrary to the common belief. This is
consistent with our recent result that the JE is also a result only for
reversible processes.
