Hypothesis: Coupling the continuum approach with a statistical one may help in the development of a generic thermodynamic model to theoretically analyse the variations of interfacial tension and subsequent deformation of an interface between a pair of fluids under a field exposure. In this direction, the local variations of interfacial tension due to the redistribution of interfacial molecules have been expressed as the functions of the molecular interaction potentials for a variety of externally applied fields. Numerical Experiments: Two continuum-statistical models for interfacial tension have been developed by choosing two different types of molecular interaction potentials. The proposed analytical models have been successfully integrated with the Cahn-Hilliard and Navier-Stokes framework before solving them numerically using computational tools. Findings: Effects of field exposure on the redistribution of the molecules and the molecular interaction potentials can be correlated to the local variations of the interfacial tension and interfacial deformations. The calculations related to the temperature dependence of interfacial thickness and interfacial tension matches well with the experimental data. The simulated results show a nearly accurate prediction of the pre-existing experimental and theoretical results on interfacial deformation under electric, magnetic and optical fields. (c) 2020 Elsevier Inc. All rights reserved.