Thermodynamics of condensed matter with strong pressure-energy correlations

TL;DR

This paper demonstrates that liquids and solids with strong pressure-energy correlations exhibit predictable thermodynamic behavior, including invariant structure along isomorphs and a density-dependent temperature function, supported by molecular dynamics simulations.

Contribution

It introduces a theoretical framework linking strong pressure-energy correlations to thermodynamic invariances and provides a new equation of state for such systems.

Findings

Isomorphs are described by h(ρ)/T=const.

Density-scaling exponent depends only on density.

A Grüneisen-type equation of state applies.

Abstract

We show that for any liquid or solid with strong correlation between its $NVT$ virial and potential-energy equilibrium fluctuations, the temperature is a product of a function of excess entropy per particle and a function of density, $T=f(s)h(\rho)$. This implies that 1) the system's isomorphs (curves in the phase diagram of invariant structure and dynamics) are described by $h(\rho)/T={\rm Const.}$, 2) the density-scaling exponent is a function of density only, 3) a Gr{\"u}neisen-type equation of state applies for the configurational degrees of freedom. For strongly correlating atomic systems one has $h(\rho)=\sum_nC_n\rho^{n/3}$ in which the only non-zero terms are those appearing in the pair potential expanded as $v(r)=\sum_n v_n r^{-n}$. Molecular dynamics simulations of Lennard-Jones type systems confirm the theory.