2014/12/08 by Felix Fabis, Daniel Berg, Fabis, Felix +5
Materials Science · Mathematics · Physics and Astronomy · #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #Material Dynamics and Properties #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #astro-ph.CO #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1412.2572
16 pages, 15 figures
arxiv created 2014/12/08 · openalex publication_date 2014/12/08 · arxiv updated 2014/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It was recently shown by Bartelmann et al. how correlated initial conditions can be introduced into the statistical field theory for classical particles pioneered by Das and Mazenko. In this paper we extend this development from the canonical to the grand canonical ensemble for a system satisfying statistical homogeneity and isotropy. We do this by translating the probability distribution for the initial phase space coordinates of the particles into an easy diagrammatic representation and then using a variant of the Mayer cluster expansion to sum over particle numbers. The grand canonical generating functional is then used in a structured approach to the derivation of the non-interacting cumulants of the two core collective fields, the density ρ and the response field B. As a side-product we find several theorems pertaining to these cumulants which will be useful when investigating the interacting regime of the theory in future work.