Related papers: Dynamical Exclusion of Probability and Energy Cons…
The stochastic differential equations for a model of dissipative particle dynamics with both total energy and total momentum conservation in the particle-particle interactions are presented. The corresponding Fokker-Planck equation for the…
In standard nonrelativistic quantum mechanics the expectation of the energy is a conserved quantity. It is possible to extend the dynamical law associated with the evolution of a quantum state consistently to include a nonlinear stochastic…
In some cases, it is possible to show the conservation of energy by using equations of motion in mechanics. By considering these results, some people can think that the conservation of energy is the result of equations of motion or Newton's…
In the present work foundations of the law of the energy conservation and the introduction of particles in the classical electrodynamics are discussed. We pay attention to a logic error which takes place at an interpretation of the…
A principle of information conservation is shown in abstract terms to rule out probabilistic physical laws, necessitating the existence of state trajectories. It furthermore provides a geometric-thermodynamic mechanism for the appearance of…
Conservation laws are discussed in conjunction with quantum-mechanical indeterminacies of the corresponding observables. The considered examples show that the connections between energy and its indeterminacy may be quite intricate. The…
In this paper, we introduce the Schrodinger equation with a general kinetic energy operator. The conservation law is proved and the probability continuity equation is deducted in a general sense. Examples with a Hermitian kinetic energy…
We consider the statistical irreversibility and its compatibility with the reversible dynamics. The role played by the observation is analyzed in detail. It makes our previous proof for the second law of thermodynamics clearer. On this…
The conservation laws of nonrelativistic and relativistic systems are reviewed and some simple illustrations are provided for the restrictive nature of the relativistic conservation law involving the center of energy compared to the…
We show that the law of energy conservation with the fact of matter stability imply the existence of energy complementary to that given by the function of states of interacting systems and treated, with the environment, the function of…
Suppose an initial state is coupled to a continuum of energy states. The population of the initial state is expected to decrease with time, but is the decrease monotonic? The occupation probability of the initial state is the survival…
For nonlinear Schroedinger equations with a power nonlinearity, a new approach to derive the conservation law of the momentum and the pseudo conformal conservation law is obtained. Since this approach does not contain approximating…
Modified versions of the Schr\"{o}dinger equation have been proposed in order to incorporate the description of measurement processes into the mathematical structure of quantum theory. Typically, these proposals introduce new physical…
We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure…
Properties of the fractional Schrodinger equation have been studied. We have proven the hermiticity of fractional Hamilton operator and established the parity conservation law for the fractional quantum mechanics. As physical applications…
In electrostatics, we can use either potential energy or field energy to ensure conservation of energy. In electrodynamics, the former option is unavailable. To ensure conservation of energy, we must attribute energy to the electromagnetic…
In relativistic quantum field theory with local interactions, charge is locally conserved. This implies local conservation of probability for the Dirac and Klein-Gordon wavefunctions, as special cases; and then in turn for non-relativistic…
We propose a nonlinear modification of the Schr\"{o}dinger equation that possesses the main properties of this equation such as the Galilean invariance, the weak separability of composite systems, and the homogeneity in the wave function.…
It is shown that in the complex trajectory representation of quantum mechanics, the Born's Psi^{\star}\Psi probability density can be obtained from the imaginary part of the velocity field of particles on the real axis. Extending this…
The principle of energy conservation leads to a generalized choice of transition probability in a piecewise adiabatic representation of quantum(-classical) dynamics. Significant improvement (almost an order of magnitude, depending on the…