A remarkable thermodynamic fermion-boson symmetry is found for the canonical ensemble of ideal quantum gases in harmonic oscillator potentials of odd dimensions. The bosonic partition function is related to the fermionic one extended to negative temperatures, and vice versa. PACS: 05.30.-d; 05.30.Ch; 05.30.Fk; 05.30.Jp

It has been recently pointed out that a definition of geometric entropy using a partition function in a conical space does not in general lead to positive definite quantity. We clarify especially for a scalar field with non-minimal coupling the origin of the anomalous behavior from the viewpoint of canonical formulation.

We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative variables. In particular this isomorphism singles out a canonical new basis of the symmetric functions in noncommutative variables which would be an analogue of the Schur function basis for this bialgebra.

Recursion relations are used to exactly calculate the partition function of a canonical ensemble in which all additive charges as well as the total isospin are strictly conserved. The ensemble can consist of particles that obey either classical or quantum statistics. Recursion relations are also employed to compute observables such as multiplicity distributions and isospin fluctuations.

We show that for every positive integer d, every downwards closed subtree T of d without terminal nodes and every finite weakly embedded subtree A of T there is a finite list of equivalence relations on Em(T ) with the property that for every other equivalence relation E on Em(T ) there is a strongly embedded subtree S ⊆ T of height ω, such that E Em(S) is equal to one of the equivalence relati...

A (set) partition of [n] = {1, 2, . . . , n} is a collection of disjoint subsets, called blocks, of [n] whose union is [n]. We will write a partition as a sequence of blocks (B1, B2, . . . , Bk) such that min(B1) < min(B2) < · · · < min(Bk), for instance, ({1, 4, 8}, {2, 5, 9}, {3}, {6, 7}). Let π = (B1, B2, . . . , Bk) be a partition of [n]. The canonical word of π is the word a1a2 · · · an, w...

The thermodynamics of the discrete nonlinear Schrödinger equation in vicinity infinite temperature is explicitly solved microcanonical ensemble by means large-deviation techniques. A first-order phase transition between a thermalized and condensed (localized) one occurs at infinite-temperature line. Inequivalence statistical ensembles characterizes phase, where grand-canonical representation do...

The canonical NLT partition function of a quasi-one dimensional (q1D) one-file system equal hard disks Pergamenshchik [19] provides an analytical description the thermodynamics and ordering in this (a pore) as linear density Nd/L where d is disk diameter. We derive formulae for distance dependence translational pair distribution distances between next neighbor disks, then demonstrate their use ...

A simple relationship of the form ZBH = |Ztop| is conjectured, where ZBH is a supersymmetric partition function for a four-dimensional BPS black hole in a Calabi-Yau compactification of Type II superstring theory and Ztop is a second-quantized topological string partition function evaluated at the attractor point in moduli space associated to the black hole charges. Evidence for the conjecture ...