Distribution function

In molecular kinetic theory in physics, a particle's distribution function is a function of seven variables, ${\displaystyle f(x,y,z,t;v_{x},v_{y},v_{z})}$, which gives the number of particles per unit volume in single-particle phase space. It is the number of particles per unit volume having approximately the velocity ${\displaystyle (v_{x},v_{y},v_{z})}$ near the place ${\displaystyle (x,y,z)}$ and time ${\displaystyle (t)}$. The usual normalization of the distribution function is

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