Statistical mechanics and thermodynamics of magnetic and dielectric systems based on magnetization and polarization fluctuations: Application of the quasi-Gaussian entropy theory

Abstract

Theoretical equations of state for temperature and electromagnetic field dependence of fluid systems, based on the quasi-Gaussian entropy theory On the use of the quasi-Gaussian entropy theory in noncanonical ensembles. I. Prediction of temperature dependence of thermodynamic propertiesThe quasi-Gaussian entropy ͑QGE͒ 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 2 , the two-dimensional Ising spin model, and the simulated extended simple point charge ͑SPC/E͒ 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 function͒ gives the best description. MnCl 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.

Study of a water-graphene capacitor with molecular density functional theory

“…Results for the permittivity r are presented in Table I for different values of applied potential. At low voltage, we obtain a value of r = 68.1 in agreement with previous values computed by MD by several groups [24][25][26]. When the applied potential increases, the computed dielectric constant decreases, which is a known effect due to saturation of the dielectric material [4,24].…”

Water response to intense electric fields: A molecular dynamics study

“…We considered the external electric field as acting on each atom in the simulation domain without depolarization terms, i.e., under tinfoil boundary conditions [Yeh and Berkowitz, ; Apol et al, ].…”

Theoretical equations of state for temperature and electromagnetic field dependence of fluid systems, based on the quasi-Gaussian entropy theory

“…In this article we will use the same general notation of electromagnetic ͑em͒ properties as in Ref. 6 ͑hereafter referred to as I͒. For an ellipsoidal system containing N molecules at temperature T and volume V, with a homogeneous external electromagnetic field F 0 aligned along one of the ellipsoidal axes, the canonical partition function is given by 6 Qϭ ͚ n e Ϫ␤͓E n ͑ 0 ͒ ϪM n ЈF 0 ϩ 1…”

“…So far the QGE theory provided theoretical models for the thermodynamics as a function of temperature, [1][2][3][4] density, 5 pressure, 5 and external field, 6 by modeling the dis-tributions of appropriate macroscopic fluctuations by ''quasi-Gaussian'' distributions, i.e., via the convolution of distributions corresponding to identical and statistically independent subsystems. 1,6 Application of the QGE theory to many different systems showed that relatively simple models can describe with high accuracy the thermodynamics of both solids 3 and fluids. 1,4,7,8 In this paper we will illustrate how the QGE theory can be extended towards theoretical models that describe the thermodynamics as a function of two state variables ͑''bivariate'' models͒.…”