Equations of State for Simple Liquids from the Gaussian Equivalent Representation Method

Abstract

Within the framework of Gaussian equivalent representation method a new procedure of obtaining equations of state for simple liquids is discussed in some technical details. The developed approach permits one to compute partition and distribution functions for simple liquids with arbitrary form of the central two-body potential of inter-molecular interaction. The proposed approach might become of great use for computing thermodynamic and structural quantities of simple particle and polymer systems. We believe that this technique can also provide an interesting possibility to reduce the sign problem of other methods of computer simulation based on a functional integral approach. *

The phonon theory of liquid thermodynamics

“…Starting from the earlier proposals30, this approach was developed in several directions (see, e.g., Refs 2331323334…”

“…Starting from the earlier proposals 30 , this approach was developed in several directions (see, e.g., Refs. 2 3 31 32 33 34 ), and can be used to calculate the energy of simple liquids where interactions are pair and short-ranged and correlations are two-body as is the case in, for example, noble liquids or hard-sphere models. On the other hand, the calculations become intractable in general case 3 33 , particularly when interactions and correlations become complex (e.g., many-body) as in the liquids discussed above, precluding the calculation of c v and, consequently, understanding and interpreting experimental data.…”

The Frenkel Line: a direct experimental evidence for the new thermodynamic boundary

“…We explain the origin of the structural crossovers across the Frenkel line in the framework of the phonon theory of liquids using molecular dynamics (MD) simulations, and relate its origin to the change of thermodynamic properties of the supercritical state. The experimental results presented here are of great interest to the ongoing effort in elucidating various properties of disordered matter [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39].…”

Thermodynamic behaviour of supercritical matter

“…The statistical description of liquids, in comparison with the solid and gas phases, is incomplete. The problem of formulating a rigorous mathematical description of liquids has always been regarded as much more difficult than that of the kinetic theory of gases or solid-state theory, stimulating the ongoing research [1][2][3][4][5][6][7][8][9]. Due to the simultaneous presence of strong interactions and large atomic displacements, common models and approximations used for gases and solids, do not apply to liquids.…”