Several questions in the statistical mechanics of non-Hamiltonian systems are discussed. The theory of differential forms on the phase space manifold is applied to provide a fully covariant formulation of the generalized Liouville equation. The properties of invariant volume elements are considered, and the nonexistence in general of smooth invariant measures noted. The time evolution of the ge...

We construct a numerical scheme based on the Liouville equation of geometric optics coupled with the Geometric Theory of Diffraction (GTD) to simulate the high frequency linear waves diffracted by a half plane. We first introduce a condition, based on the GTD theory, at the vertex of the half plane to account for the diffractions, and then build in this condition as well as the reflection bound...

The Liouville-von Neumann master equation models closed quantum spin systems that arise in Nuclear Magnetic Resonance applications. In this paper, an efficient and robust computational framework to solve exact-controllability problems governed by the Liouville-von Neumann master equation, that models control quantum spin systems, is presented. The proposed control framework is based on a new op...