In this paper we discuss the thermodynamics of apparent horizon of an n-dimensional Friedmann-Robertson-Walker (FRW) universe embedded in an (n+1)-dimensional AdS spacetime. By using the method of unified first law, we give the explicit entropy expression of the apparent horizon of the FRW universe. In the large horizon radius limit, this entropy reduces to the n-dimensional area formula, while...

In this paper we compute leading order correction due to small statistical fluctuations around equilibrium, to the Cardy-Verlinde entropy formula (which is supposed to be an entropy formula of conformal field theory in any dimension) of a Topological Reissner-Nordstrom black hole in de Sitter space. ∗E-mail: [email protected]

The relative entropy description of Holevo-Schumacher-Westmoreland (HSW) classical channel capacities is applied to single qubit quantum channels. A simple formula for the relative entropy of qubit density matrices in the Bloch sphere representation is derived. The formula is combined with the King-Ruskai-Szarek-Werner qubit channel ellipsoid picture to analyze several unital and non-unital qub...

Atar, Chowdhary and Dupuis have recently exhibited a variational formula for exponential integrals of bounded measurable functions in terms of Rényi divergences. We develop a variational characterization of the Rényi divergences between two probability distributions on a measurable space in terms of relative entropies. When combined with the elementary variational formula for exponential integr...

This paper is concerned with the entropy of an action of a countable torsion-free abelian group G by continuous automorphisms of a compact abelian group X. A formula is obtained that expresses the entropy in terms of the Mahler measure of a greatest common divisor, complementing earlier work by Einsiedler, Lind, Schmidt and Ward. This leads to a uniform method for calculating entropy whenever G...

We give an elementary derivation of the entropy production formula of [JP1]. Using this derivation we show that the entropy production of any normal, stationary state is zero.

This paper deals with the problem of finding the range of entropy values resulting from actions of discrete amenable groups by automorphisms of compact abelian groups. When the acting group G is locally normal, we obtain an entropy formula and show that the full range of entropy values [0,∞] occurs for actions of G. We consider related entropy range problems, give sufficient conditions for zero...

Shannon’s source entropy formula is not appropriate to measure the uncertainty of non-stationary processes. In this paper, we propose a new entropy measure for non-stationary processes, which is greater than or equal to Shannon’s source entropy. The maximum entropy of the non-stationary process has been considered, and it can be used as a design guideline in cryptography.

We generalize the results of hep-th/0008140 to the case of the (n+ 1)-dimensional closed FRW universe satisfying a general equation of state of the form p = wρ. We find that the entropy of the universe can no longer be expressed in a form similar to the Cardy formula, when w 6= 1/n. As a result, in general the entropy formula does not coincide with the Friedmann equation when the conjectured bo...