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

Abstract

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

References in corpus (2)

• Origins of Taylor's power law for fluctuation scaling in complex systems
• Networks with given two-point correlations: hidden correlations from degree correlations

Cited by in corpus (7)

• Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases
• The microscopic meaning of grand potential: cluster properties of the one-dimensional lattice gas
• Effects of cell-cell adhesion on migration of multicellular clusters
• Moduli space of logarithmic states in critical massive gravities
• Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework
• Exact expression for the number of states in lattice models
• Bell polynomials in the series expansions of the Ising model