Partition Function of the Model of Perfect Gas of Clusters for Interacting Fluids
Abstract
The last paper of A. Fronczak presents a new, combinatorial approach to the model of perfect gas of clusters of interacting fluids. In the paper the enumerative properties and combinatorial meaning of Bell polynomials have been used to reveal some properties of systems described by grand canonical ensemble. In this paper, an exact proof of one of the important assertions from the work mentioned above is given. The assertion states that for the system in which one can distinguish k non interacting clusters the canonical partition function is given by Bell polynomial of the derivatives of the grandthermodynamic potential with respect to the fugacity. Some possible applications of the considered theorem are presented.
 Publication:

Reports on Mathematical Physics
 Pub Date:
 August 2013
 DOI:
 10.1016/S00344877(14)600069
 Bibcode:
 2013RpMP...72...85S