Related papers: Legendre transforms for electrostatic energies

We study either fully visible and restricted Boltzmann machines with sub-Gaussian random weights and spherical or Gaussian priors. We prove the free energies of the spherical and Gaussian models are related by a Legendre transformation.…

An extension of the Legendre transform to non-convex functions with vanishing Hessian as a mix of envelope and general solutions of the Clairaut equation is proposed. Applying this to systems with constraints, the procedure of finding a…

In this paper we present the formulation of relativistic electrodynamics (independent of the reference frame and of the chosen system of coordinates in it) that uses the Faraday bivector field F. This formulation with F field is a…

We consider a simple nonlinear (quartic in the fields) gauge-invariant modification of classical electrodynamics, which possesses a regularizing ability sufficient to make the field energy of a point charge finite. The model is exactly…

In this paper a class of classical Hamiltonian systems is geometrically formulated. This class is such that a Hamiltonian can be written as the sum of a kinetic energy function and a potential energy function. In addition, these energy…

This work revisits the classical concept of electric energy and suggests that the common definition is likely to generate large errors when dealing with nanostructures. For instance, deriving the electrostatic energy in semiconductors using…

In order to understand the physical hysteresis loops clearly, we constructed a novel model, which is combined with the electric field, the temperature, and the stress as one synthetically parameter. This model revealed the shape of…

For the associated Legendre and Ferrers functions of the first and second kind, we obtain new multi-derivative and multi-integral representation formulas. The multi-integral representation formulas that we derive for these functions…

This letter describes a method for obtaining an explicit expression for the electrostatic energy of a charged elliptical infinitely thin disc. The charge distribution is assumed to be polynomial. Such explicit values for this energy are…

Based on the properties of exponential distribution families we analyze the Fisher information of the Gibbs canonical ensemble to construct a new state function for simple systems with no mechanical work. Such a function possesses nice…

A generalization of associated Legendre functions is proposed and used to describe the scattering states of the Rosen-Morse potential. The functions are then given explicit formulas in terms of the hypergeometric function, their asymptotic…

The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…

In this work we introduce a procedure to find localized structures with finite energy. We start dealing with global monopoles, and add a new contribution to the potential of the scalar fields, to balance the contribution of the angular…

Classical density-functional theory provides an efficient alternative to molecular dynamics simulations for understanding the equilibrium properties of inhomogeneous fluids. However, application of density-functional theory to multi-site…

We give a Lagrangian description of an electric charge in a field sourced by a continuous magnetic monopole distribution. The description is made possible thanks to a doubling of the configuration space. The Legendre transform of the…

A general formulation of the equilibrium state of a many-electron system in terms of a (mixed-state, ensemble) density matrix operator in the Fock space, based on the maximum entropy principle, is introduced. Various characteristic…

We describe in great generality features concerning constrained entropic, functional variational problems that allow for a broad range of applications. Our discussion encompasses not only entropies but, potentially, any functional of the…

Let X be a smooth manifold of dimension 1+n endowed with a lorentzian metric g, and let T be the electromagnetic energy tensor associated to a 2-form F. In this paper we characterize this tensor T as the only 2-covariant natural tensor…

It is generally expected from intuition that the electromagnetic force exerted on a charged particle should remain unchanged when observed in different reference frames in uniform translational motion. In the special relativity, this…

We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a…