Langevin Equations, Fokker–Planck Equations and Entropic Analysis of a Model-Independent Classical Plasma

Plasma dynamics have been studied extensively and there is a fair amount of understanding where the scientific community has reached at. However, there is still a very big gap in completely explaining plasma physics at the classical as well as the quantum level. The dynamics of plasma from an entropic approach are not very well understood or explained. There is too much chaos to account for and even a small deviation in terms of perturbations of any kind makes a sizeable difference. This study is based on the entropic approach where we take a model independent classical plasma. Then we apply Langevin equations and Fokker–Planck equations to explain the entropy generated and entropy produced. Then we study various conditions in which we apply an electric field and a magnetic field and understand the various trends in entropy changes. When we apply the electric field and the magnetic fields independently of each other and together in the plasma model, we see that there is a very important change in the increase in entropy. There are also changes in the plasma flow, but the overall flow does not drastically change since we have considered a model independent plasma. Finally, we show that there are indeed changes to the entropy in a model-independent classical plasma in the various cases as mentioned in this study.

A New Understanding of the Origin of Wave-Particle Duality in Quantum Mechanics

The wave-particle duality of quantum mechanics has always been an unsolved problem in physics. This article attempts to use one of the properties to explain the other, so as to eliminate the confusion of quantum mechanics probability waves. Specifically, this article finds that the discreteness of energy is the inherent property of all waves, so this article explains the particle nature of light from the perspective of light wave, thereby eliminating the confusion of light’s wave-particle duality; in addition, this article found that microscopic matter particles are only suitable for discussing the number of scattered particles or energy flow density, not their position and momentum, when they are forced to discuss their position and momentum, it will inevitably lead to confusion about probability waves, when only discussing the number of scattered particles or energy flow density, its volatility can be explained from the perspective of particle nature, thereby eliminating the confusion of microscopic matter particle probability waves. When the attribute of light as a wave is established, the light needs to overcome the Hamiltonian of the medium in different constraint systems (gravitational fields) during the propagation process, which will produce a universal redshift phenomenon, this can provide a new understanding of cosmic redshift; when the property of light as a wave is established, it means that the speed of light is a constant speed relative to the medium, which can provide a new understanding of the principle of constant speed of light.

Quantum Mechanics from the Energy Circulation Theory — Wave Function Showing an Energy Location in the 3D Real Space

The Schrödinger equation is one of the cores in quantum mechanics, but bears a contradiction. In the process to obtain the energy and momentum operators, the relation [Formula: see text] is used for [Formula: see text]. However, when they are applied to the Hamiltonian equation, the kinetic energy is set as [Formula: see text]. Based on the Energy Circulation Theory, we examine in this paper the quantization of motions of a particle. We clarify in which situation and for what energy we can use the relation [Formula: see text]. We derive a wave equation de novo to provide wave functions representing a concrete motion and energy distribution of a particle. The Schrödinger equation has a similar form by chance but the mass in our new equation is that of energy quantum expressed by [Formula: see text], which is common for any energies of any particles and decided only by the moving speed. A solution shows an energy location in the 3D real space even if it is expressed in complex. When a motion of a particle gets in circle, its circular frequency becomes quantized. In an atom, an electron circulates around the hidden dimensional axis, and the circulation can further rotate. We propose the quantization conditions for the electron orbiting, and derive the wave functions in concrete for S and P orbitals, which are different from current perceptions. We also demonstrate that the uncertainty principle is not valid for a motion of a particle.

Time-Invariant Superfluid Quantum Space as the Unified Field Theory

The novelty of 21st-century physics is the development of the “superfluid quantum vacuum” model, also named “superfluid quantum space” that is replacing space-time as the fundamental arena of the universe. It also represents the model that has the potential of unifying four fundamental forces of the universe. Superfluid quantum space is represented as the time-invariant fundamental field of the universe where time is merely the duration of material changes.

𝒫𝒯-Symmetric Quantum Mechanics Basics & Zeeman Effect

The non-Hermitian aspect of Quantum Mechanics has been of great interest recently. There have been numerous studies on non-Hermitian Hamiltonians written for natural processes. Some studies have even expressed the hydrogen atom in a non-Hermitian basis. In this paper, the principles of non-Hermitian quantum mechanics are applied to the time independent perturbation theory and compared with the Zeeman effect. Here, we have also shown the condition under which the Zeeman Effect results will still be true even though the Hamiltonian taken into consideration is non-Hermitian.

A Thermodynamic Formulation of Home Prices in a Monocentric City

In this work, we proposed a theoretical framework inspired by physical thermodynamics to explain the housing price distributions in monocentric cities. In the same spirit as the Alonso–Muth–Mills (AMM) model, we assume that the disposable income [Formula: see text] after renting a home a distance [Formula: see text] from the center of a city is determined by the wage [Formula: see text] generated at the point-like Central Business District (CBD), the rent [Formula: see text], and the transportation cost [Formula: see text]. Unlike in the AMM model, where the scaling exponents are phenomenological, we admitted only physically reasonable exponents for the scaling of various quantities with distance [Formula: see text] from the CBD. We then determine the equilibrium rent [Formula: see text] by requiring [Formula: see text], where we assumed for simplicity the utility function [Formula: see text] (representing the demand side) has diminishing return in [Formula: see text]. In the simplest model, the equilibrium rent is given by [Formula: see text], i.e., the scaling of [Formula: see text] with [Formula: see text] is entirely determined by [Formula: see text]. We then introduce additional home availability [Formula: see text] (representing the supply side) into the simple theory in the form of an entropic correction, [Formula: see text]. The equilibrium rent then becomes [Formula: see text]. This allows us to treat additional availability due to the two-dimensional nature of cities, as well as that due to high-rise buildings on equal footing. Finally, we compare the equilibrium theory against urban data in Singapore, London and Philadelphia. For Singapore, we find quantitative agreement between theory and data. For London, we find only qualitative agreement between theory and data because the transportation cost is zone based. For Philadelphia, the home price distribution is very different from Singapore and London, and shows clear signs of economic segregation, which is difficult to treat in our equilibrium theory.

Fundamental Values of Length, Time, and Speed

In 2018, it was shown that the electromagnetic units of the MKSA system (the ampere, coulomb, ohm, volt, etc.) can be written using the base units of the MKS system: the meter (m), kilogram (kg) and second (s). In this paper, using the conversion of units, the value of the lowest speed of movement in nature is calculated. It is shown that the value of the gravitational constant is determined by the values of the speed of light in a vacuum and the elementary speed. It is obtained a new formula for the law of universal gravitation, which is completely analogous to Coulomb’s law. It is shown that the system of the fundamental units of mass, length, and time is the system of the natural units, built on the universal constants [Formula: see text] and [Formula: see text]).

An Alternative Approach of the Dark Energy Beyond the Equation of State

Several concepts have been proposed to explain the mystic nature of dark energy and the accelerating universe. Among them, geometrical dark energy is one such class that is based on the scalar curvature, and another type is based upon the “equation of state”. Also, another model suggests that neutrino rest-mass interaction is responsible for the “equation of state” with constant energy density. In this work, we have investigated another dark energy approach which is based on the illusive mass of the photon and a new geometrical perspective. Photon reveals its illusive mass behavior when it interacts with the surface of matter, i.e., photon manifests itself into different forms of mass. Hence, photon might hide some of its energy due to this new characteristic. This photon’s energy is embedded in the form of a curvature dependent complex number and could be considered as the new form of dark energy. Hence, we propose that the dark energy might be hiding in the photon’s illusive form and could pave the way towards unravelling the secrets of the dark energy of the universe and hence the accelerating universe.

Galactic Evolution Showing a Constant Circulating Speed of Stars in a Galactic Disc without Requiring Dark Matter

It is an unsolved mystery that the rotation velocity of a galactic disc is same at any radial distances. The presence of dark matter is expected, but not observed. Here we propose a novel scheme for the evolution of the initial cosmic energy to current galaxies. According to the energy circulation theory, which we previously reported, the fundamental force works based on momentums. Antiparallel movements of energy pieces form a circulation. Due to the space expansion, the initial energy circulations separate and decompose to smaller level circulations; to galactic seeds, stellar seeds, and smallest energy circulations. The internal circulating velocity of a galactic seed is inherited to the circulating speed of stellar seeds in a ring. The intra-circulation interaction by the fundamental force keeps the stellar seeds to circulate at the initial speed, which does not alter by the space expansion. The new scheme meets the galaxy rotation curve without requiring dark matter.