where μ i is the chemical potential per particle for a type i particle, and N i is the number of such particles. The last term can also be written as μ i d n i (with d n i 0 the number of moles of component i added to the system and, in this case, μ i the molar chemical potential) or as μ i d m i (with d m i the mass of component i added to the system and, in this case, μ i the specific chemical potential).