相关论文: The origin of variational principles

Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt,…

This paper investigates the dynamics of nonholonomic mechanical systems, focusing on fundamental variational assumptions and the role of the transpositional rule. We analyze how the Cetaev condition and the first variation of constraints…

We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…

A non-local hidden variables theory for non-relativisitic quantum theory is presented, which gives a realist completion of quantum mechanics, in the sense of a complete description of individual events. The proposed fundamental theory is an…

In mechanics, common energy principles are based on fixed boundary conditions. However, in bridge engineering structures, it is usually necessary to adjust the boundary conditions to make the structure's internal force reasonable and save…

The paper investigates a systematic approach to modeling in nonequilibrium thermodynamics by focusing upon the notion of interconnections, where we propose a novel Lagrangian variational formulation of such interconnected systems by…

A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number…

Selfdual variational principles are introduced in order to construct solutions for Hamiltonian and other dynamical systems which satisfy a variety of linear and nonlinear boundary conditions including many of the standard ones. These…

A principle is proposed according to which the dynamics of a quantum particle in a one-dimensional configuration space (OCS) is determined by a variational problem for two functionals: one is based on the mean value of the Hamilton…

Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…

We review some techniques from non-linear analysis in order to investigate critical paths for the action functional in the calculus of variations applied to physics. Previous attempts to analyse when these are minima ex- ist, but mainly…

Using Onsager's variational principle, we derive dynamical equations for a nonequilibrium active system with odd elasticity. The elimination of the extra variable that is coupled to the nonequilibrium driving force leads to the…

We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence…

Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…

Using the mathematical theory of shape calculus as tool, we perform a rigorous investigation of the virtual work principle for the computation of electromagnetic forces in static settings. The main goal is to shed light on the widely held…

The spin-statistics connection, quantum gravity and other physical considerations suggest that classical space-time topology is not an immutable attribute and can change in quantum physics. The implementation of topology change using…

This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the…

A variation of fundamental constants of physics is proposed in a frame of static universe. It is shown when the velocity of light increases (decreases) the Planck's constant increases (decreases) and mass of bodies decreases (increases).…

We formulate symmetric versions of classical variational principles. Within the framework of non-smooth critical point theory, we detect Palais-Smale sequences with additional second order and symmetry information. We discuss applications…

On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…