In molecular kinetic theory in physics, a system's distribution function is a function of seven variables, 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 v = ( v x , v y , v z ) near the position r = ( x , y , z ) and time t . The usual normalization of the distribution function is n ( r , t ) = ∫ ∫ f ( r , v , t ) d v x d v y d v z , N ( t ) = ∫ ∫ n ( r , t ) d x d y d z , where N is the total number of particles and n is the number density of particles – the number of particles per unit volume, or the density divided by the mass of individual particles.