R. F. Streater

Classical and quantum probability

We follow the development of probability theory from the beginning of the last century, emphasizing that quantum theory is really a generalization of this theory. The great achievements of probability theory, such as the theory of processes, generalized random fields, estimation theory, and information geometry, are reviewed. Their quantum versions are then described.

Detailed balance and quantum dynamical maps

Let T be a stochastic map on a -algebra , and a faithful state. Let be the induced action of T on the GNS Hilbert space , and its adjoint on . We say T obeys detailed balance II if is also induced by a stochastic map. In that case we prove that is a contraction on commuting with the modular operator. The relation of this idea to microscopic reversibility is discussed. An entropy estimate is presented.

ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY

We show that, in finite dimensions, the only monotone metrics for which the (+1) and (-1) affine connections are mutually dual are constant multiples of Bogoliubov-Kubo-Mori metric

Windowed radon transforms, analytic signals, and the wave equation

Abstract . The act of measuring a physical signal or field suggests a generalization of the wavelet transform that turns out to be a windowed version of the Radon transform. A reconstruction formula is derived which inverts this transform. A special choice of window yields the “Analytic-Signal transform” (AST), which gives a partially analytic extension of functions from R n to C n . For n 1, this reduces to Gabors classical definition of “analytic signals.” The AST is applied to the wave equation, giving an expansion of solutions in terms of wavelets specifically adapted to that equation and parametrized by real space and imaginary time coordinates (the Euclidean region).

The Soret and Dufour Effects in Statistical Dynamics

We set up a discrete space–time dynamical model of molecules with thermalized kinetic energy and repulsive cores, in an external potential. The model obeys the first and second laws of thermodynamics. The continuum limit, obtained using a Maple program, gives rise to coupled reaction–diffusion equations for the density and temperature fields. The system obeys Onsager symmetry and exhibits the Soret and Dufour effects.

Quantum Orlicz Spaces in Information Geometry

AbstractLet H0 be a selfadjoint operator such that Tr

A gas of Brownian particles in statistical dynamics

e^{\beta H_0}

Dynamics of Brownian particles in a potential

is of trace class for some