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

Abstract

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 MnCl2, 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. MnCl2 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.