It is a widely accepted principle that a thermodynamically reversible desalination process should consume the Gibbs free energy of separation. This principle has been shown in reverse osmosis and has important practical implications in reducing its energy consumption. Capacitive deionization (CDI) with carbon electrodes, a desalination process based on electrical double layer (EDL) formation, should also follow such a principle when it operates in a thermodynamically reversible way. Inspired by a previous thermodynamic analysis on a three-stage reversible CDI process using the Gouy-Chapman-Stern model, we conducted a thermodynamic analysis of a four-stage reversible CDI cycle using the modified Donnan model. This analysis better reflects the cyclic nature of practical CDI operations and account for the significant EDL overlap in nanosized micropores of realistic CDI electrodes. Our analysis of CDI cycles with different separations and final discharge voltages shows that the electrical work to complete a four-stage cycles is numerically exactly identical to the Gibbs free energy of separation, as long as the cycle is operated in a thermodynamically reversible manner. (C) 2017 Elsevier Inc. All rights reserved.