The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium;...

The Poisson–Boltzmann equation describes the distribution of the electric potential in solution in the direction normal to a charged surface. This distribution...

In statistical mechanics, Boltzmann's equation (also known as the Boltzmann–Planck equation) is a probability equation relating the entropy S {\displaystyle...

Ludwig Eduard Boltzmann ForMemRS (/ˈbɒltsmən/, US also /ˈboʊl-, ˈbɔːl-/, Austrian German: [ˈluːdvɪɡ ˈbɔltsman]; 20 February 1844 – 5 September 1906) was...

The Stefan–Boltzmann law, also known as Stefan's law, describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature...

The Boltzmann constant (kB or k) is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic...

natural consequence of the kinetic equation derived by Boltzmann that has come to be known as Boltzmann's equation. The H-theorem has led to considerable...

different interpretation of the lattice Boltzmann equation is that of a discrete-velocity Boltzmann equation. The numerical methods of solution of the...

charge density follows a Boltzmann distribution, then the Poisson–Boltzmann equation results. The Poisson–Boltzmann equation plays a role in the development...

Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann....

The quantum Boltzmann equation, also known as the Uehling–Uhlenbeck equation, is the quantum mechanical modification of the Boltzmann equation, which gives...

de Saint-Venant Boltzmann equation Cauchy momentum equation Cauchy stress tensor Chapman–Enskog theory Churchill–Bernstein equation Coandă effect Computational...

The Williams–Boltzmann equation, also known as the Williams spray equation is a kinetic equation modeling the statistical evolution of evaporating or...

equations Boltzmann equation Convection–diffusion equation Klein–Kramers equation Kolmogorov backward equation Kolmogorov equation Langevin equation Master...

an alternative to the Boltzmann equation in the case of Coulomb interaction. When used with the Vlasov equation, the equation yields the time evolution...

is the Boltzmann constant. A simple derivation of the Boltzmann relation for the electrons can be obtained using the momentum fluid equation of the two-fluid...

physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius...

superposition principle. Nevertheless, the two equations can be combined to produce the Poisson–Boltzmann equation. ∇ 2 ψ j ( r ) = − 1 ϵ 0 ϵ r ∑ i { n i (...

Ludwig Boltzmann, in the development of the atomistic backgrounds of the macroscopic transport processes, introduced the Boltzmann equation, which has...

In statistical mechanics, Maxwell–Boltzmann statistics describes the distribution of classical material particles over various energy states in thermal...

In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution) is a probability distribution or probability measure...

parabolic partial differential equations, fluid mechanics, Boltzmann equations, and dispersive partial differential equations. A function u(x, y, z) of three...

theory provides a framework in which equations of hydrodynamics for a gas can be derived from the Boltzmann equation. The technique justifies the otherwise...

First, Vlasov argues that the standard kinetic approach based on the Boltzmann equation has difficulties when applied to a description of the plasma with...

which derives expressions for the viscosity of a dilute gas from the Boltzmann equation. Viscosity in gases arises principally from the molecular diffusion...

Richard Arnold. The Collisionless Boltzmann equation, also called the Vlasov Equation is a special form of Liouville' equation and is given by: ∂ f ∂ t + v...

expressions for thermal conductivity starting from the Boltzmann equation. The Boltzmann equation, in turn, provides a statistical description of a dilute...

study of the connections between interacting particle systems, the Boltzmann equation, and fluid mechanics. In 2008 she was awarded the European Mathematical...

differential equations involved in statistical mechanics, specifically the Boltzmann equation, where, with Laurent Desvillettes, he was the first to prove how quickly...

difference) coefficients are equal. For many kinetic systems, like the Boltzmann equation or chemical kinetics, the Onsager relations are closely connected...