scholarly journals Rigorous Derivation of a Ternary Boltzmann Equation for a Classical System of Particles

2021 ◽  
Author(s):  
Ioakeim Ampatzoglou ◽  
Nataša Pavlović
Keyword(s):  
Boltzmann Equation ◽  
Classical System ◽  
Rigorous Derivation ◽  
System Of Particles

scholarly journals The Relativistic Boltzmann Equation and Two Times

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 804
Author(s):  
L. P. Horwitz
Keyword(s):  
Boltzmann Equation ◽  
Monotonic Function ◽  
Relativistic Boltzmann Equation ◽  
Pair Annihilation ◽  
System Of Particles ◽  
Normal Particle ◽  
Invariant Parameter ◽  
Relativistic Framework

We discuss a covariant relativistic Boltzmann equation which describes the evolution of a system of particles in spacetime evolving with a universal invariant parameter τ . The observed time t of Einstein and Maxwell, in the presence of interaction, is not necessarily a monotonic function of τ . If t ( τ ) increases with τ , the worldline may be associated with a normal particle, but if it is decreasing in τ , it is observed in the laboratory as an antiparticle. This paper discusses the implications for entropy evolution in this relativistic framework. It is shown that if an ensemble of particles and antiparticles, converge in a region of pair annihilation, the entropy of the antiparticle beam may decreaase in time.

scholarly journals On the validity of the Boltzmann equation for short range potentials

2014 ◽  
Vol 26 (02) ◽  
pp. 1450001 ◽  
Author(s):  
M. Pulvirenti ◽  
C. Saffirio ◽  
S. Simonella
Keyword(s):  
Boltzmann Equation ◽  
Short Range ◽  
Hard Spheres ◽  
Classical System ◽  
Short Range Potential ◽  
Point Particles ◽  
Smooth Potential ◽  
Grad Limit ◽  
Repulsive Potentials ◽  
Short Times

We consider a classical system of point particles interacting by means of a short range potential. We prove that, in the low-density (Boltzmann–Grad) limit, the system behaves, for short times, as predicted by the associated Boltzmann equation. This is a revisitation and an extension of the thesis of King [9] (that appeared after the well-known result of Lanford [10] for hard spheres) and of a recent paper by Gallagher et al. [5]. Our analysis applies to any stable and smooth potential. In the case of repulsive potentials (with no attractive parts), we estimate explicitly the rate of convergence.

The Simplest Patterns of Interpenetrated Honeycomb Layers – Counter examples to the Minimal Transitivity Principle?

2018 ◽  
Author(s):  
Igor Baburin
Keyword(s):  
Crystal Engineering ◽  
Structural Chemistry ◽  
Broad Context ◽  
Rigorous Derivation ◽  
New Approach

The paper calls attention to the most symmetric interpenetration patterns of honeycomb layers. To the best of my knowledge, such patterns remained unknown so far. In my contribution a rigorous derivation of such patterns is given that makes use of a new approach to interpenetrating nets. The results are presented in a broad context of structural chemistry and crystal engineering.

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