Related papers: Lagrangian and Hamiltonian Mechanics for Probabili…
We present a formulation of classical statistical mechanics based on a Lagrangian description on the tangent bundle. In this approach, a Wick rotation from real time to imaginary time is employed as a technical device that facilitates the…
In this study, Hamiltonian and Lagrangian theories, which are mathematical models of mechanical systems, are structured on the horizontal and the vertical distributions of tangent and cotangent bundles. In the end, the geometrical and…
The statistical properties of velocity and acceleration fields along the trajectories of fluid particles transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. We present…
Reparametrization invariant Lagrangian theories with higher derivatives are considered. We investigate the geometric structures behind these theories and construct the Hamiltonian formalism in a geometric way. The Legendre transformation…
The mathematical formalism of Quantum Mechanics is derived or "reconstructed" from more basic considerations of probability theory and information geometry. The starting point is the recognition that probabilities are central to QM: the…
We formulate the Riemannian calculus of the probability set embedded with $L^2$-Wasserstein metric. This is an initial work of transport information geometry. Our investigation starts with the probability simplex (probability manifold)…
We discuss the dynamics of a particular two-dimensional (2D) physical system in the four dimensional (4D) (non-)commutative phase space by exploiting the consistent Hamiltonian and Lagrangian formalisms based on the symplectic structures…
We study the statistical mechanics of a general Hamiltonian system in the context of symplectic structure of the corresponding phase space. This covariant formalism reveals some interesting correspondences between properties of the phase…
In this study, Lagrangian and Hamiltonian systems, which are mathematical models of mechanical systems, were introduced on the horizontal and the vertical distributions of tangent and cotangent bundles. Finally, some geometrical and…
Submanifolds of a manifold are described as sections of a certain fiber bundle that enables one to consider their Lagrangian and (polysymplectic) Hamiltonian dynamics as that of a particular classical field theory. In particular, their…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
A path integral formalism for non-equilibrium systems is proposed based on a manifold of quasi-equilibrium densities. A generalized Boltzmann principle is used to weight manifold paths with the exponential of minus the information…
The standard Hamiltonian machinery, being applied to field theory, leads to infinite-dimensional phase spaces. It is not covariant. In this article, we present covariant finite-dimensional multimomentum Hamiltonian formalism for field…
We consider solutions of Lagrangian variational problems with linear constraints on the derivative. These solutions are given by curves $\gamma$ in a differentiable manifold $M$ that are everywhere tangent to a smooth distribution $\mathcal…
In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a…
The Lagrangian description of mechanical systems and the Legendre Transformation (considered as a passage from the Lagrangian to the Hamiltonian formulation of the dynamics) for point-like objects, for which the infinitesimal configuration…
Although the post-Newtonian Lagrangian formalism is widely used in relativistic dynamical and statistical studies of test bodies moving around arbitrary mass distributions, the corresponding general Hamiltonian formalism is still relatively…
We propose a generalization of Heisenberg picture quantum mechanics in which a Lagrangian and Hamiltonian dynamics is formulated directly for dynamical systems on a manifold with non--commuting coordinates, which act as operators on an…
We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and…
A natural geometric framework is proposed, based on ideas of W. M. Tulczyjew, for constructions of dynamics on general algebroids. One obtains formalisms similar to the Lagrangian and the Hamiltonian ones. In contrast with recently studied…