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 study the increase in per-sample differential entropy rate of random sequences and processes after being passed through a non minimum-phase (NMP) discrete-time, linear time-invariant (LTI) filter G. For LTI discrete-time filters and random processes, it has long been established that this entropy gain, G(G), equals the integral of log ∣ ∣G(e) ∣ ∣. It is also known that, if the first sample o...

Let (M, g) be a compact Riemannian manifold with universal covering M̃ . The simplest asymptotic invariant which can be associated to (M, g) is the exponential growth rate h(g) of volume on the universal covering, called the volume entropy. If B r (p) denotes the geodesic ball of radius r about p ∈ M̃ and volg(B r (p)) describes its volume with respect to the Riemannian metric g lifted to M̃ then ...

Let (G, μ) be a discrete group with a generating probability measure. Nevo shows that if G has property (T) then there exists an ε > 0 such that the Furstenberg entropy of any (G, μ)-stationary space is either zero or larger than ε. Virtually free groups, such as SL2(Z), do not have property (T). For these groups, we construct stationary actions with arbitrarily small, positive entropy. This co...

We study the entropy of entanglement of the ground state in a wide family of one-dimensional quantum spin chains whose interaction is of finite range and translation invariant. Such systems can be thought of as generalizations of the XY model. The chain is divided in two parts: one containing the first consecutive L spins; the second the remaining ones. In this setting the entropy of entangleme...

We consider measures on locally homogeneous spaces Γ\G which are invariant and have positive entropy with respect to the action of a single diagonalizable element a ∈ G by translations, and prove a rigidity statement regarding a certain type of measurable factors of this action. This rigidity theorem, which is a generalized and more conceptual form of the low entropy method of [Lin2, EKL] is us...

The thermodynamic functions such as enthalpy, H°, Gibbs free energy, G°, and entropy, S°, of Arginine and Lysine amino acids were theoretically studied at different polar solvents by using ²Gaussian o3², software. First, the structural optimization of isolated Arginine and Lysine were done in the gas phase by applying the Density Functional Theory (B3LYP) level ...

the thermodynamic functions such as enthalpy (h), gibbs free energy (g) and entropy (s) of serineand threonine amino acids were theoretically studied at different condition (solvents andtemperatures) by using gussian o3, software. first, the structural optimization of isolated serine andthreonine were done in the gas phase by using the hartree-fock (hf) level of theory with 3-21g, 6-31g and 6-3...

Time-of-flight ~TOF! inelastic neutron-scattering spectra were measured on b-cerium ~double hcp! and g-cerium ~fcc! near the phase-transition temperature. Phonon densities of states ~DOS! and crystal-field levels were extracted from the TOF spectra. A softening of the phonon DOS occurs in the transition from bto g-cerium, accounting for an increase in vibrational entropy of DSvib 5(0.0960.05)kB...

Let G be a discrete group which admits an amenable action on a compact space and γ ∈ Aut(G) be an automorphism. We define a notion of entropy for γ and denote the invariant by ha(γ). This notion is dual to classical topological entropy in the sense that if G is abelian then ha(γ) = hTop(γ̂) where hTop(γ̂) denotes the topological entropy of the induced automorphism γ̂ of the (compact, abelian) dual...