Distribution function (physics)

In molecular kinetic theory in physics, a system's distribution function is a function of seven variables, ${\displaystyle f(t,x,y,z,v_{x},v_{y},v_{z})}$, 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 ${\displaystyle \mathbf {v} =(v_{x},v_{y},v_{z})}$ near the position ${\displaystyle \mathbf {r} =(x,y,z)}$ and time ${\displaystyle t}$.