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The Maxwell–Boltzmann distribution is a result of the kinetic theory of gases, which provides a simplified explanation of many fundamental gaseous properties, including pressure and diffusion. [3] The Maxwell–Boltzmann distribution applies fundamentally to particle velocities in three dimensions, but turns out to depend only on the speed ...
Maxwell–Boltzmann statistics is used to derive the Maxwell–Boltzmann distribution of an ideal gas. However, it can also be used to extend that distribution to particles with a different energy–momentum relation , such as relativistic particles (resulting in Maxwell–Jüttner distribution ), and to other than three-dimensional spaces.
In a plasma, the Boltzmann relation describes the number density of an isothermal charged particle fluid when the thermal and the electrostatic forces acting on the fluid have reached equilibrium. In many situations, the electron density of a plasma is assumed to behave according to the Boltzmann relation, due to their small mass and high mobility.
A thermal neutron is a free neutron with a kinetic energy of about 0.025 eV (about 4.0×10 −21 J or 2.4 MJ/kg, hence a speed of 2.19 km/s), which is the energy corresponding to the most probable speed at a temperature of 290 K (17 °C or 62 °F), the mode of the Maxwell–Boltzmann distribution for this temperature, E peak = k T.
The general equation can then be written as [6] = + + (),. where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the diffusion of particles, and "coll" is the collision term – accounting for the forces acting between particles in collisions.
The analogues of these equations in the canonical ensemble are the barometric formula and the Maxwell–Boltzmann distribution, respectively. In the limit , the microcanonical and canonical expressions coincide; however, they differ for finite . In particular, in the microcanonical ensemble, the positions and velocities are not statistically ...
Maxwell–Boltzmann may refer to: Maxwell–Boltzmann statistics, statistical distribution of material particles over various energy states in thermal equilibrium;
For a canonical ensemble that is quantum mechanical and discrete, the canonical partition function is defined as the trace of the Boltzmann factor: = (^), where: tr ( ∘ ) {\displaystyle \operatorname {tr} (\circ )} is the trace of a matrix;