We prove a theorem which generalizes Poisson convergence for sums of independent random variables taking the values 0 and 1 to a type of “Gibbs convergence” for strongly correlated random variables. The theorem is then used to develop a lattice-to-continuum theory for statistical mechanics.

Main ideas of the differential geometry on affine bundles are presented. Affine counterparts of Lie algebroid and Poisson structures are introduced and discussed. The developed concepts are applied in a frame-independent formulation of the time-dependent and the Newtonian mechanics. MSC (2000): 37J05, 53A40, 53D99, 55R10, 70H99.

Some types of first integrals for Hamiltonian Nambu-Poisson vector fields are obtained by using the notions of pseudosymmetries. In this theory, the homogeneous Hamilto-nian vector fields play a special role and we point out this fact. The differential system which describe the SU (2)-monopoles is given as example. The paper ends with two appendices.

In this paper, using the Hojman construction, we give examples of various Poisson brackets which differ from those which are usually analyzed in Hamiltonian mechanics. They possess a nonmaximal rank, and in the general case an invariant measure and Casimir functions can be globally absent for them.

<p style='text-indent:20px;'>In this note, we propose a slightly different proof of Gallavotti's theorem ["Statistical Mechanics: A Short Treatise", Springer, 1999, pp. 48-55] on the derivation linear Boltzmann equation for Lorentz gas with Poisson distribution obstacles in Boltzmann-Grad limit.</p>

In the light of computational chemistry, based on morpholinium cation-based Ionic Liquid, their different types of physical, chemical, and biological properties is highlighted. The physical properties are evaluated through the Density Functional Theory (DFT) of Molecular Mechanics and also examine the chemical and biological properties. The difference between Highest Occupied Molecular Orbital ...

After setting up a general model for supersymmetric classical mechanics in more than one dimension we describe systems with centrally symmetric potentials and their Poisson algebra. We then apply this information to the investigation and solution of the supersymmetric Coulomb problem, specified by an 1 |x| repulsive bosonic potential. PACS: 45.50.-j; 11.30.Pb

The orbit method of Kirillov is used to derive the p-mechanical brackets [25]. They generate the quantum (Moyal) and classical (Poisson) brackets on respective orbits corresponding to representations of the Heisenberg group. The extension of p-mechanics to field theory is made through the De Donder–Weyl Hamiltonian formulation. The principal step is the substitution of the Heisenberg group with...

We prove that the Jacobi identity for the generalized Poisson bracket is satisfied in the generalization of Heisenberg picture quantum mechanics recently proposed by one of us (SLA). The identity holds for any combination of fermionic and bosonic fields, and requires no assumptions about their mutual commutativity. ∗ Submitted to Nuclear Physics B

Three one-parameter probability families; the Poisson, normal and binomial distributions, are put into a group theoretic context in order to obtain Bayes posterior distributions on their respective parameter spaces. The families are constructed according to methods used in quantum mechanics involving coherent states. This context provides a method for obtaining noninformative prior measures.