Entropy and Its Quantum Thermodynamical Implication for Anomalous Spectral Systems

The state function entropy and its quantum thermodynamical implication for two typical dissipative systems with anomalous spectral densities are studied by investigating on their low-temperature quantum behavior. In all cases it is found that the entropy decays quickly and vanishes as the temperature approaches zero. This reveals a good conformity with the third law of thermodynamics and provides another evidence for the validity of fundamental thermodynamical laws in the quantum dissipative region.Comment: 10 pages, 3 figure

Benzyl 2,5-dioxopyrrolidin-1-yl carbonate

The asymmetric unit of the title compound, C12H11NO5, contains two independent mol­ecules with similar geometric parameters but different orientations of the phenyl rings. The mol­ecular packing is stabilized by weak nonclassical C—H⋯O hydrogen-bonding inter­actions

Infinite Hopf family of elliptic algebras and bosonization

Elliptic current algebras E_{q,p}(\hat{g}) for arbitrary simply laced finite dimensional Lie algebra g are defined and their co-algebraic structures are studied. It is shown that under the Drinfeld like comultiplications, the algebra E_{q,p}(\hat{g}) is not co-closed for any g. However putting the algebras E_{q,p}(\hat{g}) with different deformation parameters together, we can establish a structure of infinite Hopf family of algebras. The level 1 bosonic realization for the algebra E_{q,p}(\hat{g}) is also established.Comment: LaTeX, 11 pages. This is the new and final versio