A Simple Derivation of Crooks Relation

Abstract

The link between properties of a system at equilibrium, in particular free energy difference, to the fluctuations in the work performed during non-equilibrium process is called Crooks relation. This relation, which is a measure of the grade of irreversibility of a process, was elegantly derived based on the equations of motion for a set of particles along with the formal solution of the evolution equation using a distribution function, both solved in a classical and a stochastic way. This technical note, reports on a simple derivation of Crooks formula based on the energy balance and entropy generation in a system undergoing a process in which fluctuations are not neglected.