From equilibrium to non-equilibrium statistical mechanics of liquids

TL;DR

This paper reviews the fundamental concepts of statistical mechanics for liquids, emphasizing the extension from equilibrium to non-equilibrium states, with applications to rheology and viscoelasticity of glass- and gel-forming liquids.

Contribution

It provides a general framework and a concrete example for describing non-equilibrium properties of liquids from first principles.

Findings

Extension of equilibrium relations to non-equilibrium conditions.

Application to rheological and viscoelastic properties.

Insights into aging and transient states in liquids.

Abstract

Relevant and fundamental concepts of the statistical mechanical theory of classical liquids are ordinarily introduced in the context of the description of thermodynamic equilibrium states. This makes explicit reference to probability distribution functions of \emph{equilibrium} statistical ensembles (canonical, microcanonical, ...) in the derivation of general and fundamental relations between inter-particle interactions and measurable macroscopic properties of a given system. This includes, for instance, expressing the internal energy and the pressure as functionals of the radial distribution function, or writing transport coefficients (diffusion constant, linear viscosity, ...) in terms of integral relations involving both, static and dynamic auto-correlation functions (density-density, stress-stress, ...). Most commonly, however, matter is not in thermodynamic equilibrium, and this calls for the extension of these relations to out-of-equilibrium conditions with the aim of understanding, for example, the time-dependent transient states during the process of equilibration, or the aging of glass- and gel-forming liquids during the formation of non-equilibrium amorphous solid states. In this work we address this issue from both, a general perspective and an illustrative concrete application focused on the first principles description of rheological and viscoelastic properties of glass- and gel-forming liquids.