## 1 Introduction  
With advancements in the field of nanotechnology, two-phase liquid-vapor problems are increasingly more present in a wide range of nanofluidic processes, such as capillary evaporation, condensation and cavitation inside nanochannels [1, 2], two-phase nanofluid flows [3, 4, 5], fluid transport through membranes [6, 7, 8] and other porous materials [9], and nanoscale droplet and bubble formation and annihilation [10, 11], just to name a few. Such nanoscale processes are also accompanied by the phase transition processes in the vicinity of the liquid-vapor interphase region, namely, evaporation and condensation, which play an important role in flow development and dynamics. Therefore, the nanoscale evaporation and condensation processes have become a popular research topic in recent years due to its value in practical nanofluidic applications. The evaporation/condensation rate can be predicted by other relationships, such as the Hertz-Knudsen (HK) or Schrage relationships, which evaluate the net mass evaporation/condensation fluxes through the phase transition interface with given liquid and vapor conditions in the vicinity of the interface [12, 13]. These relationships were derived within the framework of the kinetic theory of masses (KTG) assuming the Maxwell-Boltzmann (MB) or shifted MB velocity distribution near the interface [14]. However, these relationships use the so-called evaporation and condensation coefficients, which are unknown parameters and, therefore, must be evaluated from experimental measurements. The problem is that the experimentally measured coefficient values tend to disagree with each other for various fluids, with the most notorious such case being water, for which the condensation/evaporation coefficients have been found to vary by 3 orders of magnitude in the studies by different researchers [15; 16; 17; 18]. Arguably, such discrepancies can be attributed to experimental conditions, which are difficult or impossible to measure in evaporation/condensation experiments; for example, the temperature jumps in the Knudsen layer with spatial lengths being in the same order of magnitude as the molecular mean free path [19; 20; 21], and the velocity distribution functions of evaporating/condensing atoms at the vicinity of the interface [22]. To overcome the experimental difficulties, the molecular dynamics (MD) simulations have been used to investigate evaporation/condensation processes. The main appeal of the MD simulation method is that it provides a resolution at the molecular level as the evaporation/condensation coefficients can be estimated from the mass fluxes evaluated directly from molecular trajectories at the interface [23]. According to the mass conservation at the interface (see Figure 1, the outgoing from the interface into the vapor side atom mass flux \(J_{out}\) consists of the spontaneously evaporating atom mass flux \(J_{sp}\) and reflected atom mass flux \(J_{r}\). On the other hand, the colliding with the interface vapor atom mass flux \(J_{col}\) consists of condensing atom mass flux \(J_{c}\) and reflecting atom mass flux \(J_{r}\). The evaporation and condensation coefficients correspond to the phase change probabilities of atoms and are defined as ratios [24; 25]:  
\[\sigma_{e}=\frac{J_{sp}}{J_{out}}=\frac{J_{sp}}{J_{sp}+J_{r}} \tag{1}\]  
and  
\[\sigma_{c}=\frac{J_{c}}{J_{col}}=\frac{J_{c}}{J_{c}+J_{r}} \tag{2}\]  
In the liquid-vapor thermal equilibrium condition, the condensation mass flux \(J_{c}\) becomes equal to spontaneous evaporation \(J_{sp}\) and, consequently, the evaporation coefficient becomes equal to the condensation coefficient. In such a case, both coefficients can be regarded simply as the mass accommodation coefficient (MAC) [14]. The coefficient names can be used interchangeably, and the MAC will be regarded as the evaporation coefficient throughout this paper.