Thermophysics-Informed Phenomenological Framework for Molten Material Self-Organization in Laser Remelting-Based Surface Polishing: Conceptualization and Preliminary Analysis

The goal of laser polishing (LP) is to improve the surface quality of functional parts, components, and assemblies. LP is a complex nonlinear thermophysical process, in which laser radiation induces localized melting of a material with an initially rough surface topography. During LP, the thermodynamic state evolves dynamically due to transient melt flow, heat transfer, and rapid solidification within the laser–material interaction zone. A smooth surface is formed through the interplay between surface tension-driven flow, which promotes energy minimization, and nonequilibrium effects associated with melting and solidification. From the perspective of self-organization, LP can be interpreted as an open system driven by energy input, where complex material redistribution leads to the evolution of surface topography. In this work, the self-organization of molten material is analyzed using chaos-based descriptors, including the Lyapunov exponent, phase portrait, approximate entropy, and the Hurst exponent, calculated from measured surface topographies before and after laser polishing. The results show that LP acts as a spatial low-pass filter, reducing high-frequency surface components associated with micromilling marks, and exhibits a directional bias in material redistribution relative to the laser scanning direction. Among the evaluated descriptors, the Lyapunov and Hurst exponents demonstrate consistent behaviors, indicating their suitability as robust indicators of surface state in post-process analysis. For the investigated conditions (Inconel 718), a laser fluence of 158.3 mJ/cm2 provided the best-achieved surface quality, corresponding to an improvement in surface roughness (Ra) of approximately 70% and the lowest Lyapunov exponent of 1.966 and highest Hurst exponent of 0.859. This study demonstrates that chaos-based analysis of surface topography provides a phenomenological framework for assessing process stability and surface evolution, offering a basis for thermophysics-informed development of LP in applications such as mold and die manufacturing.