## Quick Reference

An equation used in the study of a collection of particles in nonequilibrium statistical mechanics, particularly their transport properties. The Boltzmann equation describes a quantity called the distribution function, *f*, which gives a mathematical description of the state and how it is changing. The distribution function depends on a position vector *r*, a velocity vector *v*, and the time *t*; it thus provides a statistical statement about the positions and velocities of the particles at any time. In the case of one species of particle being present, Boltzmann's equation can be written ∂*f*/∂*t*+*a***.**(∂*f*/∂*v*)+*v***.**(∂*f*/∂*r*) = (∂*f*/∂*t*)_{coll}, where *a* is the acceleration of bodies between collisions and (∂*f*/∂*t*)_{coll} is the rate of change of *f*(*r*,*v*,*t*) due to collisions. The Boltzmann equation can be used to calculate transport coefficients, such as conductivity. The equation was proposed by Ludwig Boltzmann in 1872.

∂*f*/∂*t*+*a***.**(∂*f*/∂*v*)+*v***.**(∂*f*/∂*r*) = (∂*f*/∂*t*)_{coll}

*Subjects:*
Chemistry — Physics.

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