Gaussian and non-Gaussian fluctuations in pure classical fluids

Abstract

The particle number, energy, and volume probability distributions in the canonical, isothermalisobaric, grand canonical, and isobaric-isenthalpic ensembles are investigated. In particular, we consider Gaussian and non-Gaussian behavior and formulate the results in terms of a single expression valid for all the ensembles employing common, experimentally accessible, thermodynamic derivatives. This is achieved using Fluctuation Solution Theory to help manipulate derivatives of the entropy. The properties of the distributions are then investigated using available equations of state for fluid water and argon. Purely Gaussian behavior is not observed for any of the state points considered here. A set of simple measures, involving thermodynamic derivatives, indicating non-Gaussian behavior is proposed. A general expression, valid in the high temperature limit, for small energy fluctuations in the canonical ensemble is provided. Published by AIP Publishing. [http://dx

Gas or Liquid? The Supercritical Behavior of Pure Fluids

“…Fluctuations, however, are ensemble-dependent, and, in particular, the particle number fluctuations adopted here appear specific to the GCE. Fortunately, as we have recently shown, 74 the pair and triplet fluctuations in different ensembles are related to the same thermodynamic derivatives in a simple manner. For instance, the isothermal compressibility in the GCE is given by eq 2.…”

“…Figure 1 shows that the particle number distribution is not Gaussian for a real fluid at any state point. 74 Indeed, the triplet fluctuations quantified by C 111 are always positive in the gas phase (B 11 = C 111 = ρ 1 for an ideal gas) and always negative in the liquid phase. 60 Hence, particle addition is more probable than removal for gases, whereas particle removal is more probable than addition in liquids, presumably due to the higher particle densities involved.…”

“…Hence, the fluctuations can easily be extracted from the relevant experimental data. 76 The pair particle fluctuations are given by, 57,72,74…”

“…Note that “1” will be used as a shorthand for “ N 1 ” in the subscripts of B , C , and D . The above quantities were obtained by repeated differentiation of the GCE partition function with respect to the chemical potential, ,, and the choice of this particular form of excess energy is outlined elsewhere . The pair ( B ’s), triplet ( C ’s), and quadruplet ( D ’s) fluctuations can be related to integrals over the pair, triplet, and quadruplet spatial molecular correlation functions if desired. , The pair correlations can also be expressed in terms of a short-range direct correlation function using the Ornstein–Zernike equation. , However, neither of these extensions is required for the present analysis.…”

Experimental investigation of triplet correlation approximations for fluid water

“…In a series of recent studies, we have been investigating triplet correlations in fluids and liquid mixtures as characterized by the triplet fluctuations observed for an open system [14, 31–34]. This has involved the use of Fluctuation Solution Theory (FST) [35], an extension of the Kirkwood-Buff (KB) theory of solutions [36], to relate the thermodynamic properties of fluids to the fluctuations expected for an equivalent system in the Grand Canonical Ensemble (GCE).…”