Boltzmann equation

The Boltzmann equation is given by (Ref.1 Eq 1 Chap. IX)

${\frac {\partial f_{i}}{\partial t}}=-{\mathbf {u} }_{i}\cdot {\frac {\partial f_{i}}{\partial {\mathbf {r} }}}-{\mathbf {F} }_{i}\cdot {\frac {\partial f_{i}}{\partial {\mathbf {u} }_{i}}}+\sum _{j}C(f_{i},f_{j})$

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle } is an external force and the function C() represents binary collisions.

See also

• H-theorem

References

1. Sybren R. De Groot and Peter Mazur "Non-Equilibrium Thermodynamics", Dover Publications