/ 98 08 08 5 v 1 1 4 A ug 1 99 8 Gravitational Entropy and Global Structure

ar X iv : h ep - t h / 98 08 08 5 v 2 2 5 A ug 1 99 8 Gravitational Entropy and Global Structure

The underlying reason for the existence of gravitational entropy is traced to the impossibility of foliating topologically non-trivial Euclidean spacetimes with a time function to give a unitary Hamiltonian evolution. In d dimensions the entropy can be expressed in terms of the d − 2 obstructions to foliation, bolts and Misner strings, by a universal formula. We illustrate with a number of exam...

ar X iv : m at h / 98 08 06 5 v 1 [ m at h . Q A ] 1 4 A ug 1 99 8 QUANTUM DETERMINANTS AND QUASIDETERMINANTS

ua nt - p h / 98 08 02 3 v 1 1 4 A ug 1 99 8 Probability and Entropy in Quantum Theory ∗

Entropic arguments are shown to play a central role in the foundations of quantum theory. We prove that probabilities are given by the modulus squared of wave functions, and that the time evolution of states is linear and also unitary.

ar X iv : a st ro - p h / 98 08 03 4 v 1 5 A ug 1 99 8 Weighing Superclusters

We present a summary report on a detailed study of the mass and dynamical state of the Corona Borealis supercluster using the largest redshift survey of this object to date. Extensive N-body experiments are performed on simulated superclusters in both critically-flat and low-density cosmological models to test the robustness and errors of the mass estimators used on the data. From the redshifts...

ar X iv : m at h / 99 08 08 0 v 1 [ m at h . D S ] 1 6 A ug 1 99 9 Topological Entropy and ε - Entropy for Damped Hyperbolic Equations

We study damped hyperbolic equations on the infinite line. We show that on the global attracting set G the ε-entropy (per unit length) exists in the topology of W 1,∞. We also show that the topological entropy per unit length of G exists. These results are shown using two main techniques: Bounds in bounded domains in position space and for large momenta, and a novel submultiplicativity argument...