Related papers: The energy conservation law in classical electrody…
A systematic study of energy conservation for extended magnetohydrodynamic (MHD) models that include Hall terms and electron inertia is performed. It is observed that commonly used models do not conserve energy in the ideal limit, i.e.,…
In these notes we discuss the conservation of the energy for weak solutions of the two-dimensional incompressible Euler equations. Weak solutions with vorticity in $L^\infty_t L^p_x$ with $p\geq 3/2$ are always conservative, while for less…
The straightforward application of energy and linear momentum conservation to the absorption/emission of photons by atoms allows to establish the essential features of laser cooling of two levels atoms at low laser intensities. The lowest…
We study a recently derived fully relativistic kinetic model for spin-1/2 particles. Firstly, the full set of conservation laws for energy, momentum and angular momentum are given, together with an expression for the (non-symmetric)…
The field-dependent equilibrium thermodynamics is derived with two methods: either by using the potential formalism either by the statistical method. Therefore, Pontrjagin's extremum principle of control theory is applied to an extended…
The explanation of the apparent universality of thermodynamics points toward the extension of the usual conceptual background of the second law. Arguments are collected that a basic guiding idea of stability of thermodynamic equilibrium…
The second law of classical thermodynamics, based on the positivity of the entropy production, only holds for deterministic processes. Therefore the Second Law in stochastic quantum thermodynamics may not hold. By making a fundamental…
We argue that statistical mechanics of systems with relaxation implies breaking the energy function of systems into two having different transformation rules. With this duality the energy approach incorporates the generalized vortex forces.…
This paper extends the foundational concept to second-order quantum correlation tensors, representing intensity-intensity correlations.As their application in diverse optical field experiments gaining importance, we investigate conserved…
This paper gives a general treatment and proof of the direct conservation law method presented in Part I. In particular, the treatment here applies to finding the local conservation laws of any system of one or more partial differential…
We present examples of simple electromagnetic systems in which energy, linear momentum, and angular momentum exhibit interesting behavior. The systems are sufficiently simple to allow exact solutions of Maxwell's equations in conjunction…
The Conservation of Energy plays a pivotal part in the development of the physical sciences. With the growth of computation and the study of other discrete token based systems such as the genome, it is useful to ask if there are…
The leapfrog integrator is widely used because of its excellent stability in molecular dynamics simulation. This is recognized as being due to the existence of a discrete variational structure of the equations. We introduce a modified…
In this paper, energy-preserving methods are formulated and studied for solving charged-particle dynamics. We first formulate the scheme of energy-preserving methods and analyze its basic properties including algebraic order and symmetry.…
This is a light-hearted take at the the second law of thermodynamics.
Expected utility maximization problems in mathematical finance lead to a generalization of the classical definition of entropy. It is demonstrated that a necessary and sufficient condition for the second law of thermodynamics to operate is…
This article describes the third law of thermodynamics. This law is often poorly known and is often decried, or even considered optional and irrelevant to describe weather and climate phenomena. This, however, is inaccurate and contrary to…
Fluid dynamics accompanies with the entropy production thus increases the local temperature, which plays an important role in charged systems such as the ion channel in biological environment and electrodiffusion in capacitors/batteries. In…
Evidence implies that basic laws of thermodynamics must be tested by experiments. In this paper, an experiment is designed to measure the entropy of a system with at least one known (measurable) equation of state, especially the gas…
The concept of entropy and the correct application of the Second Law of thermodynamics are essential in order to understand the reason why quantum error correction is thermodynamically possible and no violation of the Second Law occurs…