Related papers: Difference Boltzmann Equation
A framework for relativistic thermodynamics and statistical physics is built by first exploiting the symmetries between energy and momentum in the derivation of the Boltzmann distribution, then using Einstein's energy-momentum relationship…
The existence of stationary distributions in a multicomponent Boltzmann equation using a non-additive kinetic energy composition rule for binary collisions is discussed. It is found that detailed balance is not achieved when -- in contrast…
We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity…
Bohmian mechanics represents the universe as a set of paths with a probability measure defined on it. The way in which a mathematical model of this kind can explain the observed phenomena of the universe is examined in general. It is shown…
We derive the Boltzmann equation in the context of a gravity theory with non-minimal coupling between matter and curvature. We show that as the energy-momentum tensor is not conserved in these theories, it follows a condition on the…
This article investigates the full Boltzmann equation up to second order in the cosmological perturbations. Describing the distribution of polarized radiation by a tensor valued distribution function, we study the gauge dependence of the…
The Boltzmann distribution predicts the collective behavior of systems at thermodynamic equilibrium as a function of their constituent parts. Yet most systems in nature are not at equilibrium, and a unified theory of their behavior does not…
We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal…
We briefly introduce several fundamental problems that cause the creation of Discrete Boltzmann modeling and analysis Method(DBM), corresponding solutions, the relationship and difference between DBM and traditional fluid modeling and other…
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
Dynamical symmetries of the collisionless Boltzmann transport equation, or Vlasov equation, but under the influence of an external driving force, are derived from non-standard representations of the $2D$ conformal algebra. In the case…
The lattice Boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered. Although the equation is a derivative of lattice gas automata, it…
To calculate the baryon asymmetry in the baryogenesis via leptogenesis scenario one usually uses Boltzmann equations with transition amplitudes computed in vacuum. However, the hot and dense medium and, potentially, the expansion of the…
Derivation of the canonical (or Boltzmann) distribution based only on quantum dynamics is discussed. Consider a closed system which consists of mutually interacting subsystem and heat bath, and assume that the whole system is initially in a…
Boltzmann equations are often used to study the thermal evolution of particle reaction networks. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after relativistic…
The known nonlinear kinetic equations (in particular, the wave kinetic equation and the quantum Nordheim -- Uehling -- Uhlenbeck equations) are considered as a natural generalization of the classical spatially homogeneous Boltzmann…
In this paper we explore the following question: can the probabilities constituting the quantum Boltzmann distribution, $P^B_n \propto e^{-E_n/kT}$, be derived from a requirement that the quantum configuration-space distribution for a…
In this paper the Planck function is derived in the frequency domain using the method of oscillators. It is also presented in the wavelength domain and in the wave number domain. The latter is mainly used in spectroscopy for studying…
We review Boltzmann machines and energy-based models. A Boltzmann machine defines a probability distribution over binary-valued patterns. One can learn parameters of a Boltzmann machine via gradient based approaches in a way that log…
The classical Boltzmann equation is an integro-differential equation which describes the time evolution of rarefied gas in terms of a molecular distribution function. For some kinetic problems where it is necessary to add in the Boltzmann…