# Consequences of the Detailed Balance for the Crooks Fluctuation Theorem

## TL;DR

This paper critically examines the assumptions behind the Crooks fluctuation theorem, revealing that it only applies to reversible processes and challenging its applicability to irreversible thermodynamic phenomena.

## Contribution

It clarifies the limitations of the Crooks fluctuation theorem under detailed balance, showing it is valid only for reversible processes and not for irreversible ones.

## Key findings

- CFT assumes all microstates along a trajectory have equilibrium probabilities.
- The backward trajectory definition does not return to the initial microstate.
- CFT applies only to reversible processes satisfying Kolmogorov's criterion.

## Abstract

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.