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The quasi-Gaussian entropy (QGE) theory employs the fact that a free-energy change can be written as the moment-generating function of the appropriate probability distribution function of macroscopic fluctuations of an extensive property. In this article we derive the relation between the free energy of a system in an external magnetic or electric field and the distribution of the “instantaneous” magnetization or polarization at zero field. The physical-mathematical conditions of these distributions are discussed, and for several continuous and discrete model distributions the corresponding thermodynamics, or “statistical state,” is derived. Some of these statistical states correspond to well-known descriptions, such as the Langevin and Brillouin models. All statistical states have been tested on several magnetic and dielectric systems: antiferromagnetic MnCl[sub 2], the two-dimensional Ising spin model, and the simulated extended simple point charge (SPC/E) water under an electric field. The results indicate that discrete modeling of magnetization and polarization is rather essential for all systems. For the Ising model the “discrete uniform” state (corresponding to a Brillouin function) gives the best description. MnCl[sub 2] is best described by a “symmetrized binomial state,” which reflects the two opposing magnetic sublattices. For simulated water it is found that the polarization, as well as the type of distribution of the fluctuations, is strongly affected by the shape of the system. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The quasi-Gaussian entropy (QGE) theory employs the fact that a free-energy change can be written as the moment-generating function of the appropriate probability distribution function of macroscopic fluctuations of an extensive property. By modeling this distribution, one obtains a model of free energy and resulting thermodynamics as a function of one state variable. In this paper the QGE theory has been extended towards theoretical models or equations of state (EOS’s) of the thermodynamics of semiclassical systems as a function of two state variables. Two “monovariate” QGE models are combined in the canonical ensemble: one based on fluctuations of the excess energy (the confined gamma state giving the temperature dependence) and the other based on fluctuations of the reduced electromagnetic moment [various models as derived in the preceding paper [Apol, Amadei, and Di Nola, J. Chem. Phys. 116, 4426 (2002)], giving the external field dependence]. This provides theoretical EOS’s for fluid systems as a function of both temperature and electromagnetic field. Special limits of these EOS’s are considered: the general weak-field EOS and the limit to a Curie’s law behavior. Based on experimental data of water and simulation data using the extended simple point charge (SPC/E) water model at 45.0 and 55.51 mol/dm3, the specific EOS based on a relatively simple combination of the confined gamma state model with a discrete uniform state field model accurately reproduces the dielectric properties of water at constant density, as the temperature dependence of the weak-field dielectric constant for gases and liquids, and the field dependence of the dielectric constant of liquids. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this article we investigate the applicability of the statistical Gamma state as following from the quasi-Gaussian entropy theory, where all thermodynamic properties at every temperature are obtained from the knowledge of the potential energy distribution at one temperature. We compared for a typically polar system (water) and an apolar one (methane) the experimental heat capacity and entropy data with the predictions of the theory at various densities, ranging from the almost ideal gas to typical liquids. Interestingly, the behavior of water and methane is quite similar. Low-density gases and fluid-liquid systems can be described as weakly perturbed Gamma states. For intermediate densities a more complex statistical state arises. In order to describe more accurately the fluid-liquid regime, we propose in this paper a confined Gamma state, based on the division of phase-space into two different regions: one of them described by an exact Gamma state and another very unstable one. We conclude that typical fluid-liquids can be described very well by this new Gamma state approximation. We also try to give a physical interpretation of the two parts of phase space that arise from the model. The high accuracy of the theory over a large temperature range makes the approach very suitable for the prediction of thermodynamical properties at, for example, supercritical conditions. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A new theory is presented for calculating the Helmholtz free energy based on the potential energy distribution function. The usual expressions of free energy, internal energy and entropy involving the partition function are rephrased in terms of the potential energy distribution function, which must be a near Gaussian one, according to the central limit theorem. We obtained expressions for the free energy and entropy with respect to the ideal gas, in terms of the potential energy moments. These can be linked to the average potential energy and its derivatives in temperature. Using thermodynamical relationships we also produce a general differential equation for the free energy as a function of temperature at fixed volume. In this paper we investigate possible exact and approximated solutions. The method was tested on a theoretical model for a solid (classical harmonic solid) and some experimental liquids. The harmonic solid has an energy distribution, which can be derived exactly from the theory. Experimental free energies of water and methanol could be reproduced very well over a temperature range of more than 300 K. For water, where the appropriate experimental data were available, also the energy and heat capacity could be reproduced very well. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Presents the quasi-Gaussian entropy theory in a comprehensive and consistent way, introducing a derivation of the theory suited for application to molecular systems as well as multiphase systems. System definition; Definition of reference states and excess properties; Potential energy distribution; Thermodynamic master equation; Conjugated pressure equation.

We derived a method to evaluate the liquid–vapor equilibrium pressure, with high accuracy over a large range of temperature, using the quasi-Gaussian entropy theory. The final expression that we obtain for the equilibrium pressure as a function of the temperature can be considered as a very accurate approximate solution of the Clausius–Clapeyron equation. The method was applied to water, methanol and mercury, and was compared to two usual approximations of the Clausius–Clapeyron equation. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this article we present an equation of state for fluids, based on the quasi-Gaussian entropy theory. The temperature dependence along isochores is described by a confined Gamma state, previously introduced, combined with a simple perturbation term. The 11 parameters occurring in the free energy and pressure expressions along the isochores are obtained from molecular dynamics simulation data. The equation of state has been parametrized for the Lennard-Jones fluid in the (reduced) density range 0-1.0 and (reduced) temperature range 1.0-20.0 using (partly new) NV T molecular dynamics simulation data. An excellent agreement for both energy and pressure was obtained. To test the ability to extrapolate to unknown state points, the parametrization was also performed on a smaller set of data in the temperature range 1.0-6.0. The results in the two cases are remarkably close, even in the high temperature range, and are often almost indistinguishable, in contrast to a pure empirical equation of state, like for example the modified Benedict-Webb-Rubin equation. The coexistence line agrees in general very well with Gibbs ensemble and NpT simulation results, and only very close to the critical point there are deviations. Our estimate of the critical point for both parametrizations is somewhat different from the best estimate based on Gibbs ensemble simulations, but is in excellent agreement with other estimates based on NV T simulations and integral equations. [ABSTRACT FROM AUTHOR]