There are many partition functions, but how are their results related? If the usual formal derivation, e.g., of the canonical formalism from the microcanonical formalism, works as designed, all ensembles should give us the same thermodynamics; thermodynamic potentials corresponding to various partition functions are related mutually by Legendre transformations. Therefore, for ordinary particle-...

This paper is concerned with structures of general graphs with perfect matchings. We first reveal a partially ordered structure among factor-components of general graphs with perfect matchings. Our second result is a generalization of Kotzig’s canonical partition to a decomposition of general graphs with perfect matchings. It contains a short proof for the theorem of the canonical partition. Th...

The partition function and specific heat of a system consisting of a finite number of bosons confined in an external potential are calculated in different spatial dimensions. Using the grand partition function as the generating function of the partition function, an iterative scheme is established for the calculation of the partition function of system with an arbitrary number of particles. The...

Grand canonical ensemble of small vortex loops emerging in the London limit of the effective Abelian-projected theory of the SU(3)-gluodynamics is investigated in the dilute gas approximation. An essential difference of this system from the SU(2)-case is the presence of two interacting gases of vortex loops. Two alternative representations for the partition function of such a grand canonical en...

Let g be a continuous, compactly supported function on R such that the integer translates of g constitute a partition of unity. We show that the Gabor system (g, a, b), with window g and time-shift and frequency-shift parameters a, b > 0 has no lower frame bound larger than 0 if b = 2, 3, . . . and a > 0. In particular, (g, a, b) is not a Gabor frame if g is a continuous, compactly supported wa...

In this paper we complete the algorithm DISPGB (Discussing Parametric Gröbner Basis) from the last paper by Montes, in order to obtain the Minimal Canonical Comprehensive Gröbner System (MCCGS). Given a parametric ideal, the MCCGS algorithm provides the minimal partition of the parameter space with associated Gröbner bases having the same type of solutions over each segment and provides a canon...

We calculate certain features of Bose–Einstein condensation in the ideal gas by using recurrence relations for the partition function. The grand canonical ensemble gives inaccurate results for certain properties of the condensate that are accurately provided by the canonical ensemble. Calculations in the latter can be made tractable for finite systems by means of the recurrence relations. The i...

We model a macromolecule as an infinitely long Gaussian semi-flexible polymer chain and the conformations of were realized in nano cube using cubic lattice. A modified version recursion relations is used to calculate grand canonical partition function investigate distinct thermo-dynamical properties aggregate than corresponding bulk behaviour macromolecule. Our analytical estimates on thermodyn...

A one-dimensional branching-coalescing model is considered on a chain of length L with reflecting boundaries. We study the phase transitions of this model in a canonical ensemble by using the Yang-Lee description of the non-equilibrium phase transitions. Numerical study of the canonical partition function zeros reveals two second-order phase transitions in the system. Both transition points are...

Entropy maximization subject to known expected values is extended to the case where the random variables involved may take on positive infinite values. As a result, an arbitrary probability distribution on a finite set may be realized as a canonical distribution. The Rényi entropy of the distribution arises as a natural by-product of this realization. Starting with the uniform distribution on a...