Related papers: Cauchy stress in mass distributions
Because of the mass density-dependence, an extra term should be added to the expression of pressure. However, it should not appear in that of energy according to both the general ensemble theory and basic thermodynamic principle. We give a…
Entropy is the distinguishing and most important concept of our efforts to understand and regularize our observations of a very large class of natural phenomena, and yet, it is one of the most contentious concepts of physics. In this…
Thermodynamics of ideal Fermi gas trapped in an external generic power law potential $U=\sum_{i=1} ^d c_i |\frac{x_i}{a_i}|^{n_i}$ are investigated systematically from the grand thermodynamic potential in $d$ dimensional space. These…
One of the most intriguing features of string thermodynamics is thermal duality, which relates the physics at temperature T to the physics at inverse temperature 1/T. Unfortunately, the traditional definitions of thermodynamic quantities…
The above comment http://dx.doi.org/10.1088/0953-8984/22/42/428001 and a previous letter by the same author reveal a great misunderstanding of what Eulerian and Lagrangian quantities are, and a confusion between the deformation of an…
The property that power means are monotonically increasing functions of their order is shown to be the basis of the second laws not only for processes involving heat conduction but also for processes involving deformations. In an…
A notion of "asymptotic Cauchy gain" for input/output systems, and an associated small-gain principle, are introduced. A Lyapunov-like characterization allows the computation of these gains for state-space systems, and the formulation of…
Understanding thermodynamics and statistical mechanics in the full general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the…
Much of the century-old debate surrounding the status of thermodynamics in relativity has centered on the search for a suitably relativistic temperature; recent works by Chua (2023) and Chua and Callender (forthcoming) have suggested that…
Consideration is given to the KdV equation as an approximate model for long waves of small amplitude at the free surface of an inviscid fluid. It is shown that there is an approximate momentum density associated to the KdV equation, and the…
Despite the wide usage of information as a concept in science, we have yet to develop a clear & concise scientific definition. This paper is aimed at laying the foundations for a new theory concerning the mechanics of information alongside…
The quantum mechanics is considered to be a partial case of the stochastic system dynamics. It is shown that the wave function describes the state of statistically averaged system $<\mathcal{S}_{st}>$, but not that of the individual…
The buoyancy force is the cause of ordered vertical movements in the atmosphere, therefore, the analysis of the causes and conditions of its formation is important not only for the formation of convective clouds, but also for understanding…
The basic idea of a microscopic understanding of Thermodynamics is to derive its main features from a microscopic probability distribution. In such a vein, we investigate the thermal statistics of quasi-probabilities's semi-classical…
We prove that a temperature independent mass distribution is identically zero below a mass threshold (mass gap) value, if the pressure satisfies certain inequalities. This supports the finding of a minimal mass in quark matter equation of…
Let $\pi:X\to Y$ be a factor map, where $(X,T)$ and $(Y,S)$ are topological dynamical systems. Let ${\bf a}=(a_1,a_2)\in {\Bbb R}^2$ with $a_1>0$ and $a_2\geq 0$, and $f\in C(X)$. The ${\bf a}$-weighted topological pressure of $f$, denoted…
We develop a mathematical theory for a class of compressible viscoelastic rate-type fluids with stress diffusion. Our approach is based on the concepts used in the nowadays standard theory of compressible Newtonian fluids as…
In the previous papers of the author it has been shown that the 1st law of thermodynamics in chemical reactions is the following one: dU=dQ+PdV+SUM In the present paper this theory was developed and it has been shown that the 1st law of…
The pivotal point of the paper is to discuss the behavior of temperature, pressure, energy density as a function of volume along with determination of caloric EoS from following two model: $w(z)=w_{0}+w_{1}\ln(1+z)$ & $…
The particle effective mass is often a challenging concept in solid state physics due to the many different definitions of the effective mass that are routinely used. Also, the most commonly used theoretical definition of the effective mass…