Showing papers by "David Ruelle published in 2001"
TL;DR: In this article, the authors considered a quantum spin system consisting of a finite subsystem connected to infinite reservoirs at different temperatures and proved that the rate of entropy production in such states is nonnegative.
Abstract: We consider a quantum spin system consisting of a finite subsystem connected to infinite reservoirs at different temperatures. In this setup we define nonequilibrium steady states and prove that the rate of entropy production in such states is nonnegative.
103 citations
TL;DR: In this paper, it was shown that the volume on T 3 has atomic conditional measures on the Γ's: there is a finite k such that almost every Γ carries $k$ atoms of mass 1/k.
Abstract: Let A 3 be the product of the automorphism \(\) of T 2 and of the identity on T 1. A small perturbation g of A 3 among volume preserving diffeomorphisms will have an invariant family of smooth circles Γ forming a continuous foliation of T 3. Corresponding to the vector bundle tangent to the circles Γ there is a “central” Lyapunov exponent of (g, volume), which is nonzero for an open set of ergodic g's. This surprising result of Shub and Wilkinson is complemented here by showing that the volume on T 3 has atomic conditional measures on the Γ's: there is a finite k such that almost every Γ carries $k$ atoms of mass 1/k.
98 citations
TL;DR: Non-equilibrium processes, such as heat conduction in a bar of metal, remain poorly characterized at the microscopic level, but detailed analysis of simple models can introduce a new degree of understanding.
Abstract: Non-equilibrium processes, such as heat conduction in a bar of metal, remain poorly characterized at the microscopic level. Detailed analysis of simple models can introduce a new degree of understanding.
17 citations
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TL;DR: For a small volume preserving perturbation, an exact and rigorous second-order expansion of the Lyapunov exponents was obtained in this paper, starting from a hyperbolic toral automorphism.
Abstract: Starting from a hyperbolic toral automorphism, we obtain, for a small volume preserving perturbation, an exact and rigorous second order perturbation expansion of the Lyapunov exponents.
16 citations
Posted Content•
TL;DR: In this paper, the authors present a minimal mathematical introduction to operator algebras, with physical applications in mind, and study some questions related to the quantum statistical mechanics of spin systems, with particular attention to the time evolution of infinite systems.
Abstract: The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications in mind. In Chapter 2 we study some questions related to the quantum statistical mechanics of spin systems, with particular attention to the time evolution of infinite systems. The basic reference for these two chapters is Bratteli-Robinson: Operator algebras and quantum statistical mechanics I, II. In Chapter 3 we discuss the nonequilibrium statistical mechanics of quantum spin systems, as it is currently being developped.
13 citations
TL;DR: In this article, the authors discuss entropy production in nonequilibrium steady states for infinite quantum spin systems, and show that some questions of principle remain to be clarified in this area.
Abstract: This paper discusses entropy production in nonequilibrium steady states for infinite quantum spin systems. Rigorous results have been obtained recently in this area, but a physical discussion shows that some questions of principle remain to be clarified.
2 citations
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2 citations