We study the effect of nonfactorizable background geometry on thermodynamics clustering galaxies. A canonical partition function is derived for gravitating system galaxies treated as point particles contained in cells appropriate dimensions. Various thermodynamic equations state, like Helmholtz free energy and entropy, among others, are also obtained. estimate corrected Newton law distribution ...

A bstract Motivated by the prospect of constraining microscopic models, we calculate exact one-loop corrected de Sitter entropy (the logarithm sphere partition function) for every effective field theory quantum gravity, with particles in arbitrary spin representations. In doing so, universally relate function to quotient a quasi-canonical bulk and Euclidean edge function, given integrals charac...

We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of canonical labelling of graphs with edge colourings. We then present two canonical labelling algorithms based on edge enumeration, and a third based on an exten...

We prove that the class of cluster integrable systems constructed by Goncharov and Kenyon out dimer model on a torus coincides with one defined Gekhtman, Shapiro, Tabachnikov, Vainshtein using Postnikov’s perfect networks. To end we express characteristic polynomial network’s boundary measurement matrix in terms partition function associated bipartite graph. Our main tool is flat geometry. Name...

Quantum statistical mechanics has developed primarily through two approaches, pioneered by Gibbs and Feynman, respectively. In Gibbs' method one calculates partition functions from phase-space integrations or sums over stationary states. Alternatively, in Feynman's approach, the focus is on the path-integral formulation. The Hubbard-Stratonovich transformation leads to a functional-integral for...

To understand the distribution of the Yang–Lee zeros in quantum integrable field theories we analyse the simplest of these systems given by the 2D Yang– Lee model. The grand-canonical partition function of this quantum field theory, as a function of the fugacity z and the inverse temperature β, can be computed in terms of the thermodynamics Bethe Ansatz based on its exact S-matrix. We extract t...

Abstract We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit...