Our understanding of the three basic states of matter (solids, liquids, and gases) is based on temperature and pressure phase diagrams with three phase transition lines: solid-gas, liquid-gas, and solid-liquid lines. There are analytical expressions $P\left(T\right)$ for the first two lines derived on a purely general-theoretical thermodynamic basis. In contrast, there exists no similar function for the third, melting, line (ML). Here, we develop a general two-phase theory of MLs and their analytical form. This theory predicts the parabolic form of the MLs for normal melting, relates the MLs to thermal and elastic properties of liquid and solid phases, and quantitatively agrees with experimental MLs in different system types. We show that the parameters of the ML parabola are governed by fundamental physical constants. In this sense, parabolic MLs possess universality across different systems.

• Received 7 November 2023
• Accepted 19 February 2024

DOI:https://doi.org/10.1103/PhysRevE.109.034122

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society