###### Abstract  
At the molecular scale, the definition of solid/fluid boundary is ambiguous since its defining precision is comparable to the size of the electron orbitals. It is important to figure out the sub-atomic-level solid/fluid boundary as the definition of the solid/fluid interface is related to estimating various properties such as slip length, Kapitza resistance, confined volume, thermodynamic properties, and material properties. In this work, molecular dynamics (MD) simulations were conducted to show the effects of the solid/fluid boundary on estimating thermodynamic properties. Our results reveal that the different definitions of solid/fluid boundary can cause a considerable impact on quantitative analysis and even qualitative analysis of a nanoscale system. The solid/fluid boundary for Lennard-Jones atoms is determined within sub-atomic precision via heat transfer MD simulations and microscopic heat flux relation. The result shows that solid/fluid boundary is slightly shifted to the fluid regime as the temperature increase. We suggested a mathematical expression of solid/fluid boundary of LJ atom that is theoretically estimated by ignoring the thermal vibration. The results presented in this work are expected to improve the accuracy of analyzing nanoscale phenomena as well as the continuum-based models for nanoscale heat and mass transport.  
s _Applied Sciences_  
For small systems, interfacial phenomena play a crucial role due to the large surface-to-volume ratio. However, it is difficult to access the molecular-level details of the interfacial phenomena via experiments. Because of the difficulty, molecular dynamics (MD) simulations have become an important tool to investigate the interfacial phenomena. The MD simulation provides all atomic trajectories, which can be converted into measurable macroscopic properties. Also, the thermodynamic and transport properties of both solids and liquids are well reproduced by MD simulations [17, 18, 19, 20, 21, 22]. As MD simulation allows us to investigate molecular-level details of the interfacial phenomena, it is necessary to define the solid/fluid boundary with atomic-level accuracy. The atomic-level solid/fluid boundary involves the thermal motion, the discrete nature, the interatomic force penetration. Hence, defining a boundary with atomic precision is complicated a problem.  
The followings are the definitions of solid/fluid boundary have been used during the past decades: (i) innermost solid layer (center to center) [23, 24, 25, 26, 27], (ii) midpoint between the innermost solid layer and the first adsorbed layer [9], (iii) first zero fluid density (accessible area) [28, 29], and (iv) the first peak of the adsorption layer [12, 30, 31]. The problems arising from the absence of atomic-level boundary definition have been reported in several documents. [PERSON] et al. [8] point out that the determination of velocity slip is sensitive to the defined boundary. Similarly, [PERSON] et al. [9] show the interfacial thermal resistance considerably depends on the solid/fluid boundary definition. [PERSON] et al. [10] report that the evaluations of the local properties adjacent to the solid/fluid interface are affected by the boundary definition. [PERSON] et al. [19] documented that a proper definition of the liquid/gas interface is necessary for accurate measurement of the contact angle. Despite these reported problems, there is no classical MD study on elucidating the atomic-level definition of solid/fluid boundary.  
The rest of the paper is organized as follows: we first present the details of the MD simulation. we then show the effects of the defined boundary on thermodynamic properties and material. The atomic-level boundaries for Ag-Ar, Ag-He, and Cu-Ar are estimated by heat transfer MD simulation and microscopic heat transport equation. We further study the temperature effects on the boundary definition. At the end of the article, a summary of the findings is presented.