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...

Ever since the pioneering works of Bekenstein and Hawking, black hole entropy has been known to have a quantum origin. Furthermore, it has long been argued by Bekenstein that entropy should be quantized in discrete (equidistant) steps given its identification with horizon area in (semi-)classical general relativity and the properties of area as an adiabatic invariant. This lead to the suggestio...

We prove that an ergodic free action of a countable discrete amenable group with completely positive entropy has a countable Lebesgue spectrum. Our approach is based on the Rudolph-Weiss result on the equality of conditional entropies for actions of countable amenable groups with the same orbits. Relative completely positive entropy actions are also considered. An application to the entropic pr...

Many nonlinear lattice systems exhibit high-amplitude localized structures, or discrete breathers. Such structures emerge in the discrete nonlinear Schrödinger equation when the energy is above a critical threshold. This paper studies the statistical mechanics at the transition and constructs the probability distribution in the regime where breathers emerge. The entropy as a function of the ene...