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We present a completely new approach to the problem of interacting fluids,which we believe may provide important insights into microscopic mechanismsthat lead to the occurrence of phase transitions. The approach exploitsenumerative properties and combinatorial meaning of Bell polynomials. We derivethe exact formula for probability of a general system of N particles attemperature T to consist of k weakly coupled clusters of various sizes. We alsoshow that the grand potential of the system may be considered as theexponential generating function for the number of internal states(thermodynamic probability) of these clusters. The microscopic interpretationof the grand potential is novel and surprising, especially if one recalls thatuntil now the only thermodynamic meaning of this free energy was known. We alsoderive an approximated expression for the density of states.

The microscopic meaning of grand potential resulting from combinatorial approach to a general system of particles