Related papers: Classical Analytical Mechanics and Entropy Product…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
The article is dedicated to discussion of irreversibility and foundation of statistical mechanics "from the first principles". Taking into account infinitesimal and, as it seems, neglectful for classical mechanics fluctuations of the…
A short review of basic formulas from Hamiltonian formalism in classical mechanics in the case when Lagrangian contains N time-derivatives of n coordinate variables. For non-local models N=infinity.
In this work, a methodology is proposed for formulating general dynamical equations in mechanics under the umbrella of the principle of energy conservation. It is shown that Lagrange's equation, Hamilton's canonical equations, and…
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…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the…
We show that classical mechanics can be recovered as the high-entropy limit of quantum mechanics. That is, the high entropy masks quantum effects, and mixed states of high enough entropy can be approximated with classical distributions. The…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…
The mechanism of irreversible dynamics in the systems with mixing is analyzed. The procedure of splitting of system on equilibrium subsystems and studying of dynamics of one of them under condition of its interaction with other subsystems…
It is shown that any singular Lagrangian theory: 1) can be formulated without the use of constraints by introducing a Clairaut-type version of the Hamiltonian formalism; 2) leads to a special kind of nonabelian gauge theory which is similar…
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or…
We compare two proposals for the dynamical entropy of quantum deterministic systems (CNT and AFL) by studying their extensions to classical stochastic systems. We show that the natural measurement procedure leads to a simple explicit…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
A vast concourse of events and phenomena occur in nature that may be interrelated by a entropy-maximization technique that provides a comprehensible explanation of a range of physical problems, integrating in a new framework the universal…
This paper discusses some of the modal involvements of analytical mechanics. I first review the elementary aspects of the Lagrangian, Hamiltonian and Hamilton-Jacobi approaches. I then discuss two modal involvements; both are related to…
We show that the main difference between classical and quantum systems can be understood in terms of information entropy. Classical systems can be considered the ones where the internal dynamics can be known with arbitrary precision while…
We consider a general approach to the theory of continuous media starting from Lagrangian formalism. This formalism which uses the trajectories if constituents of media is very convenient for taking into account different types of…
This work generalizes the classical metriplectic formalism to model Hamiltonian systems with nonconservative dissipation. Classical metriplectic representations allow for the description of energy conservation and production of entropy via…