Related papers: The energy conservation law in classical electrody…
Skeptics of biological evolution often claim that evolution requires a decrease in entropy, giving rise to a conflict with the second law of thermodynamics. This argument is fallacious because it neglects the large increase in entropy…
We modify Hamiltonian mechanics. We reformulate the law of conservation of energy.
We show that the no-deleting and no-cloning principles are implications of information conservation principle. This is unlike in classical physics, where cloning and deleting are possible, independently of information conservation.…
The paper [1] by Liu, Madhavan, and Tegmark sought to use machine learning methods to elicit known conservation laws for several systems. However, in their example of a damped 1D harmonic oscillator they made seven serious errors, causing…
In this paper, we use the method of Fourier analysis to derive the formula of the total energy for the Cauchy problem of the Cauchy-Navier elastodynamics wave equation describing the motion of an isotropic elastic body. The conservation law…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
Under certain conditions usually fulfilled in classical mechanics, the principle of conservation of linear momentum and Newton's third law are equivalent. However, the demonstration of this fact is usually incomplete in textbooks. We shall…
Onsager's conjecture, which relates the conservation of energy to the regularity of weak solutions of the Euler equations, was completely resolved in recent years. In this work, we pursue an analogue of Onsager's conjecture in the context…
The second law of thermodynamics places a limitation into which states a system can evolve into. For systems in contact with a heat bath, it can be combined with the law of energy conservation, and it says that a system can only evolve into…
We show that in the new description, Dirac's ``current vector'' is not related to a vector but to a tensor: the ``stress-energy tensor.'' Corresponding to Dirac's conservation law, we have the conservation laws of momentum and energy. The…
In this paper we propose an approach to the problem of two body motion in classical electrodynamics that takes into account the electromagnetic radiation and the radiation reaction forces. The resulting differential equations are solved…
The origin of electromagnetic momentum for general static charge-current distributions is examined. The electromagnetic momentum for static electromagnetic fields is derived by implementing conservation of momentum for the sum of mechanical…
This work revisits the classical concept of electric energy and suggests that the common definition is likely to generate large errors when dealing with nanostructures. For instance, deriving the electrostatic energy in semiconductors using…
The electric current conservation in a two-dimensional quantum wire under a time dependent field is investigated. Such a conservation is obtained as the global density of states contribution to the emittance is balanced by the contribution…
In this paper, we present a possible theoretical explanation for benford's law. We develop a recursive relation between the probabilities, using simple intuitive ideas. We first use numerical solutions of this recursion and verify that the…
When \lambda_{T} << d_{T}, where \lambda_{T} is the de Broglie wavelength and d_{T}, the distance of closest approach of thermal electrons, a classical analysis of the energy of a plasma can be made. In all the classical analysis made until…
In this paper we study equations of magnetic hydrodynamics with a stress tensor. We interpret this system as the generalized Euler equation associated with an abelian extension of the Lie algebra of vector fields with a non-trivial…
A recently proposed quantum mechanical criterion `concavity of energy' for the second law of thermodynamics is studied also for classical particle systems confined in a bounded region by a potential with a time-dependent coupling constant.…
Although its practical efficiency is unquestionable, it is well known that thermodynamics presents conceptual difficulties from the theoretical point of view. It is shown that the problem comes from an imperfect compatibility between the…
The problems of Classical Electrodynamics with the electron equation of motion and with non-integrable singularity of its self-field stress tensor are well known. They are consequences, we show, of neglecting terms that are null off the…