Thermodynamic formalism for transport coefficients with an application to the shear modulus and shear viscosity

TL;DR

This paper applies thermodynamic formalism to compute shear modulus and viscosity in particle systems, demonstrating fluctuation-based methods align with direct simulations and highlighting the influence of coupling strength on fluctuations.

Contribution

It introduces a fluctuation-based approach for calculating transport coefficients using thermodynamic formalism and validates it through Brownian dynamics simulations.

Findings

Fluctuations depend on coupling strength to the strain reservoir.

Fluctuation-based calculations agree with direct simulation results.

The approach is viable for numerical transport coefficient estimation.

Abstract

We discuss Onsager's thermodynamic formalism for transport coefficients and apply it to the calculation of the shear modulus and shear viscosity of a monodisperse system of repulsive particles. We focus on the concept of extensive "distance" and intensive "field" conjugated via a Fenchel-Legendre transform involving a thermodynamic(-like) potential, which allows to switch ensembles. Employing Brownian dynamics, we calculate both the shear modulus and the shear viscosity from strain fluctuations and show that they agree with direct calculations from strained and non-equilibrium simulations, respectively. We find a dependence of the fluctuations on the coupling strength to the strain reservoir, which can be traced back to the discrete-time integration. These results demonstrate the viability of exploiting fluctuations of extensive quantities for the numerical calculation of transport coefficients.