Abstract. Starting from the defining transformations of complex matrices for the SO(4) group, we construct the fundamental representation and the tensor and spinor representations of the group SO(4). Given the commutation relations for the corresponding algebra, the unitary representations of the group in terms of the generalized Euler angles are constructed. These mathematical results help us ...

The one-dimensional asymmetric exclusion process (ASEP) is a paradigm for nonequilibrium dynamics, in particular driven diffusive processes. It is usually considered in a canonical ensemble in which the number of sites is fixed. We observe that the grand-canonical partition function for the ASEP is remarkably simple. It allows a simple direct derivation of the asymptotics of the canonical norma...

A bstract We construct the canonical constitutive relations for a fluid description of system with spin current, valid in an arbitrary number dimensions absence parity breaking or time reversal terms. Our study encompasses hydrostatic partition function, entropy Kubo formula, conformal invariance, and effect charge. At some stages computation we turn on background torsion tensor which naturally...

The thermodynamic quantities of Lennard-Jones gases, evaluated till the fourth virial coefficient, are investigated for an isobaric process. A partition function in the T -P grand canonical ensemble Y (T,P,N) may be defined by the Laplace transform of the partition function Z(T,V,N) in the canonical ensemble. The Gibbs free energy is related with Y (T,P,N) by the Legendre transformation G(T,P,N...

We estimate galaxy clustering under a modified gravitational potential. In particular, the modifications in potential energy occur due to power-law and cosmological constant terms. derive canonical partition function for system of galaxies interacting such Moreover, we compute various thermodynamical equation states system. do comparative analysis order emphasize effect corrections on thermodyn...

Motivated by the recent conjecture of Ooguri, Strominger and Vafa, we compute the semi-canonical partition function of BPS black holes in N = 4 and N = 8 string theories, to all orders in perturbation theory. Not only are the black hole partition functions surprisingly simple; they capture the full topological string amplitudes, as expected from the OSV conjecture. The agreement is not perfect,...

A partition Π of the set [n] = {1, 2, . . . , n} is a collection B1, B2, . . . , Bd of nonempty disjoint subsets of [n]. The elements of a partition are called blocks. We assume that B1, B2, . . . , Bd are listed in the increasing order of their minimum elements, that is minB1 < minB2 < · · · < minBd. The set of all partitions of [n] with d blocks is denoted by P (n, d). The cardinality of P (n...