Adiabatic thermostatistics of the two parameter entropy and the role of Lambert's W-function in its applications

A unified framework to describe the adiabatic class of ensembles in the generalized statistical mechanics based on Schwammle-Tsallis two parameter (q, q') entropy is proposed. The generalized form of the equipartition theorem, virial theorem and the adiabatic theorem are derived. Each member of the class of ensembles is illustrated using the classical nonrelativistic ideal gas and we observe that the heat functions could be written in terms of the Lambert's W-function in the large N limit. In the microcanonical ensemble we study the effect of gravitational field on classical nonrelativistic ideal gas and a system of hard rods in one dimension and compute their respective internal energy and specific heat. We found that the specific heat can take both positive and negative values depending on the range of the deformation parameters, unlike the case of one parameter Tsallis entropy.Comment: 26 pages, Accepted for Publication in Physica

Super-Jordanian Quantum Superalgebra Uh(osp(2/1)){\cal U}_{h}(osp(2/1))

A triangular quantum deformation of $osp(2/1)$ from the classical $r$-matrix including an odd generator is presented with its full Hopf algebra structure. The deformation maps, twisting element and tensor operators are considered for the deformed $osp(2/1)$. It is also shown that its subalgebra generated by the Borel subalgebra is self-dual.Comment: 18 Page

Universal T-matrix, Representations of OSp_q(1/2) and Little Q-Jacobi Polynomials

We obtain a closed form expression of the universal T-matrix encapsulating the duality of the quantum superalgebra U_q[osp(1/2)] and the corresponding supergroup OSp_q(1/2). The classical q-->1 limit of this universal T-matrix yields the group element of the undeformed OSp(1/2) supergroup. The finite dimensional representations of the quantum supergroup OSp_q(1/2) are readily constructed employing the said universal T-matrix and the known finite dimensional representations of the dually related deformed U_q[osp(1/2)] superalgebra. Proceeding further, we derive the product law, the recurrence relations and the orthogonality of the representations of the quantum supergroup OSp_q(1/2). It is shown that the entries of these representation matrices are expressed in terms of the little Q-Jacobi polynomials with Q = -q. Two mutually complementary singular maps of the universal T-matrix on the universal R-matrix are also presented.Comment: 21pages, no figure; final form for publicatio

Maps and twists relating U(sl(2))U(sl(2)) and the nonstandard Uh(sl(2))U_{h}(sl(2)): unified construction

A general construction is given for a class of invertible maps between the classical $U(sl(2))$ and the Jordanian $U_{h}(sl(2))$ algebras. Different maps are directly useful in different contexts. Similarity trasformations connecting them, in so far as they can be explicitly constructed, enable us to translate results obtained in terms of one to the other cases. Here the role of the maps is studied in the context of construction of twist operators between the cocommutative and noncocommutative coproducts of the $U(sl(2))$ and $U_{h}(sl(2))$ algebras respectively. It is shown that a particular map called the `minimal twist map' implements the simplest twist given directly by the factorized form of the ${\cal R}_{h}$-matrix of Ballesteros-Herranz. For other maps the twist has an additional factor obtainable in terms of the similarity transformation relating the map in question to the minimal one. The series in powers of $h$ for the operator performing this transformation may be obtained up to some desired order, relatively easily. An explicit example is given for one particularly interesting case. Similarly the classical and the Jordanian antipode maps may be interrelated by a similarity transformation. For the `minimal twist map' the transforming operator is determined in a closed form.Comment: LaTeX, 13 page

New connection formulae for the q-orthogonal polynomials via a series expansion of the q-exponential

Using a realization of the q-exponential function as an infinite multiplicative sereis of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal polynomials such as q-Hermite, q-Laguerre and q-Gegenbauer polynomials in terms of their respective classical analogs.Comment: 14 page

Generalized boson algebra and its entangled bipartite coherent states

Starting with a given generalized boson algebra U_(h(1)) known as the bosonized version of the quantum super-Hopf U_q[osp(1/2)] algebra, we employ the Hopf duality arguments to provide the dually conjugate function algebra Fun_(H(1)). Both the Hopf algebras being finitely generated, we produce a closed form expression of the universal T matrix that caps the duality and generalizes the familiar exponential map relating a Lie algebra with its corresponding group. Subsequently, using an inverse Mellin transform approach, the coherent states of single-node systems subject to the U_(h(1)) symmetry are found to be complete with a positive-definite integration measure. Nonclassical coalgebraic structure of the U_(h(1)) algebra is found to generate naturally entangled coherent states in bipartite composite systems.Comment: 15pages, no figur

Temporal segregation between dung-inhabiting beetle and fly species

The coexistence of ecologically similar species (i.e. species utilizing the same resource) is a major topic in ecology. Communities are assembled either through the biotic interactions of ecologically similar species, e.g. competition, or by the abiotic separation of species along gradients of environmental conditions. Here, we investigated the temporal segregation, succession and seasonality of dung-inhabiting Coleoptera and Diptera that utilize an identical resource in exactly the same way. The data were collected from two temperate pastures, one in the United Kingdom and the second in the Czech Republic. There was no evident temporal separation between ecologically similar coleopterous or dipterous taxa during succession. In contrast, these two orders were almost perfectly separated seasonally in both combined and site-specific datasets. Flies were most abundant in the summer, and beetles were more abundant in the spring and autumn. Ecologically similar beetles and flies also displayed seasonal separation in both combined and site-specific data. Analyses within site-specific data sets revealed such a separation at both the order and species level. Season is therefore the main temporal axis separating ecologically similar species of dung-inhabiting insects in temperate habitats, while succession aggregates species that may have similar environmental tolerances (to e.g. dung moisture). This separation between ecologically similar taxa of beetles and flies may be attributable to either competition-based niche separation or to temperature tolerance-based habitat filtering, since flies have peak activity in warmer months while beetles have peak activity in cooler months