Description
Fluid behavior in nanoscale confinement plays an important role in many natural and technological processes. For example, water transport through biological membrane channels such as Aquaporin, chemical reactions occurring inside nanoporous catalysts, and fluid transport in energy storage or filtration membranes all involve liquids confined within extremely small spaces. At these scales, fluids often exhibit properties that differ significantly from their bulk behavior. A widely studied prototype system is water confined inside Carbon Nanotubes (CNTs), which provides a simplified model for investigating the intrinsic properties of nanoconfined fluids. Previous studies in the early 2010s proposed equations of state (EoS) describing water in CNTs with good agreement with simulations. However, these formulations are typically limited to specific geometries and molecular systems. This raises a broader question: can a general thermodynamic framework be developed to describe fluids confined in nanoscale environments of arbitrary shape? In this work, we investigate the fundamental thermodynamic properties of nanoconfined fluids from the perspective of Statistical Mechanics. We derive a generalized equation of state that relates pressure to standard thermodynamic variables and the internal energy of the system. Because internal energy depends on both molecular interactions and the geometry of the confining boundaries, the resulting framework provides a pathway for describing a wide range of confined fluid systems. This work aims to provide a fundamental theoretical basis for understanding nanoconfined fluid behavior and to support computational approaches such as Molecular Dynamics simulations in studies of nanoscale transport and materials design.