Another important class of methods are the fractional component Monte Carlo moves where gradual insertion and deletion of particles are performed through use of a coupling parameter λ with an adaptative bias potential -bearing some similarity in essence to the thermodynamic integration methods. These methods have been used in single and multicomponent systems in dense phases, as a way to improve phase equilibria simulations and to allow the direct calculation of chemical potentials and partial molar properties. In fractional component MC simulations, the number of particles is a continuous variable through λ in a way that particle insertion or deletion is done with a so-called fractional particle. More precisely, a set of Metropolis-like acceptance rules can be derived for λ: if a change of the coupling parameter occurs so that λ > 1, the current fractional component particle is converted into a real particle and a new fractional particle in inserted with coupling parameter of λ-1. Likewise, if the coupling parameter becomes λ < 0, the fractional particle is removed from the system and a remaining particle is designed as the new fractional particle with a coupling parameter of λ + 1. To further improve the convergence of these simulations, an appealing strategy is to improve the acceptance probability of particle insertions or deletions by using some local relaxation process, in order to minimize energy penalty and remove non-physical forces by collective motion in the surrounding molecules. This relaxation is typically performed through the introduction of a number of MD steps. Therein, C ¸agin and Pettitt developed an hybrid method where an MC move is used to change the composition of the system, associated with deterministic MD trajectories for relaxation. Another example of scheme has been proposed by Boinepalli and Attard 21 where a MD step in the microcanonical ensemble is performed at a given state associated to a certain value of coupling parameter λ of the current fractional molecule. For further details, we refer the interested reader to the recent and comprehensive review by Rabhari and co-workers on fractional component Monte carlo methods. Recently, Nilmeier and co-workers introduced a new type of hybrid MC move denoted nonequilibrium candidate Monte Carlo (NCMC) based on non equilibrium molecular dynamics. In this method, a candidate move is proposed through a finite-time process where the system is driven out of equilibrium, and accepted with a probability that preserves microscopic reversibility. In this process, the acceptance rule follows a Metropolis-type probability, where the total work performed during the out-of-equilibrium process is taken into account (instead of the difference of free energy). The generation of out-of-equilibrium states induces an additional computational cost, compensated by the reduced structural correlation that can occur in dense systems such as electrolytes and the versatile nature of the algorithm.