Comment on "Computation of the viscosity of a liquid from time averages of stress fluctuations"

Equilibrium fluctuations of liquid state static properties in a subvolume by molecular dynamics

System property fluctuations increasingly dominate a physical process as the sampling volume decreases. The purpose of this work is to explore how the fluctuation statistics of various thermodynamic properties depend on the sampling volume, using molecular dynamics (MD) simulations. First an examination of various expressions for calculating the bulk pressure of a bulk liquid is made, which includes a decomposition of the virial expression into two terms, one of which is the Method of Planes (MOP) applied to the faces of the cubic simulation cell. Then an analysis is made of the fluctuations of local density, temperature, pressure, and shear stress as a function of sampling volume (SV). Cubic and spherical shaped SVs were used within a spatially homogeneous LJ liquid at a state point along the melting curve. It is shown that the MD-generated probability distribution functions (PDFs) of all of these properties are to a good approximation Gaussian even for SV containing only a few molecules (∼10), with the variances being inversely proportional to the SV volume, Ω. For small subvolumes the shear stress PDF fits better to a Gaussian than the pressure PDF. A new stochastic sampling technique to implement the volume averaging definition of the pressure tensor is presented, which is employed for cubic, spherical, thin cubic, and spherical shell SV. This method is more efficient for less symmetric SV shapes.

Generalized thermodynamic and transport properties. II. Molecular liquids

In the present paper, we extend the method described in paper I [D. Bertolini and A. Tani, preceding paper, Phys. Rev. E 83, 031201 (2011)] to molecular liquids, which allows us to solve the exact kinetic equation proposed by de Schepper et al. [Phys. Rev. A 38, 271 (1988)] without approximations. In particular, generalized thermodynamic properties (enthalpy, specific heat, and thermal expansion coefficient) and transport properties (longitudinal viscosity, thermal conductivity) have been calculated for three liquids of increasing complexity, namely dimethyl sulfoxide, hydrogen fluoride, and SPC/E water. All results have been obtained by the molecular formalism as well as the atomic one, corrected for intramolecular correlations that are due to the models adopted. As done for simple liquids, the coupling between the viscous stress tensor and the energy flux vector has been calculated exactly. We also show that the Markov assumption for the dynamics related to thermal conductivity can only be adopted with caution.