## 3 Results and Discussion  
### Temperature Profile in Virtual Vacuum Simulation  
We begin this section by comparing the phase equilibria simulation temperature profile with the temperature profiles from the deletion vacuum and our proposed steady-state vacuum simulations. In both vacuum simulations, the standard temperature control scheme is used where the interface regions are simulated in the NVE ensemble, and the simulation temperature is maintained with the thermostat applied to the thermostat region, which coincides with the liquid phase [24; 26; 27; 28; 29]. The reason for the thermostat region boundaries being set below the liquid surface position is that the thermostat would not affect the evaporating atoms in the interface. The temperature profiles of all three simulations are given in Figure 5. In the phase equilibria simulation, the temperature is uniform in all regions of the simulation since the net heat and mass fluxes are zero at the liquid surfaces. Meanwhile, the temperature profiles in the vacuum simulations are non-uniform in both the liquid and interface regions. In case of the deletion vacuum simulation, the liquid region possesses a parabolic temperature profile form with temperature values above 90 K in the middle of the liquid, and the temperature values below 90 K at the liquid surface position located around coordinate \(z^{*}=0\)[14]. The parabolic shape in the liquid phase is caused by the combination of the evaporative heat sink effect, which lowers the temperature of the liquid surfaces, and the heat source in the liquid phase, which is induced by the thermostat maintaining the average simulation temperature within the thermostat region boundaries. The same temperature control approach in the constant vacuum state simulation leads to a similar problem: the temperature has a decreasing linear shape in the liquid region, which is caused by the heat sink at the right-side surface and heat source at the left-side surface due to incoming transported atoms. In both vacuum simulation cases, the temperature drops rapidly beyond the evaporating liquid surfaces because part of the thermal energy of evaporated atoms is converted to the kinetic energy of the macroscopic evaporation flow in the \(z\) axis [36]. Let us also note that the temperature profile from the constant vacuum state simulation is considerably smoothened by the greater amount of collected statistical data compared to the deletion vacuum simulation profile, in which violent fluctuations are present, especially in the interface.  
The comparison of temperature profiles in the liquid phase and near the liquid surface (as shown in Figure 5) clearly demonstrates the problem related with the commonly used temperature control approach: the spontaneous evaporation rates used to evaluate the evaporation coefficients from the phase equilibria simulations are obtained at lower surface temperatures in the virtual vacuum simulations compared to the surface temperatures in the phase equilibria simulations. Such temperature differences introduce errors in the evaporation coefficient evaluation from the perspective of molecular dynamics simulations, especially at higher temperatures where the evaporation rates scale exponentially with temperature. Hence, the following sections are focused on the vacuum simulation temperature control strategies to maintain the uniform temperature profile across the liquid phase, the errors induced by the surface temperature differences on the estimation of spontaneous evaporation rates and corresponding evaporation coefficients, and the thermostat impact on the energetic characteristics of the evaporating atoms.