# Thermodynamic heterogeneity and crossover in the supercritical state of matter

## TL;DR

This study reveals that the supercritical state of matter exhibits thermodynamic heterogeneity and a crossover, challenging the traditional view of smooth property variation without phase-like changes.

## Contribution

We identify a thermodynamic crossover in the supercritical state and propose a new definition for its relative width, linking it to the supercritical Frenkel line.

## Key findings

- Supercritical thermodynamic properties vary qualitatively at different temperatures.
- The relative width of the thermodynamic crossover is 13-20%.
- The crossover is related to the supercritical Frenkel line.

## Abstract

A hallmark of a thermodynamic phase transition is the qualitative change of system thermodynamic properties such as energy and heat capacity. On the other hand, no phase transition is thought to operate in the supercritical state of matter and, for this reason, it was believed that supercritical thermodynamic properties vary smoothly and without any qualitative changes. Here, we perform extensive molecular dynamics simulations in a wide temperature range and find that a deeply supercritical state is thermodynamically heterogeneous, as witnessed by different temperature dependence of energy, heat capacity and its derivatives at low and high temperature. The evidence comes from three different methods of analysis, two of which are model-independent. We propose a new definition of the relative width of the thermodynamic crossover and calculate it to be in the fairly narrow relative range of 13-20\%. On the basis of our results, we relate the crossover to the supercritical Frenkel line.