We study the statistical mechanics of a finite-dimensional non-linear Hamiltonian system (a chain of anharmonicoscillators) coupled to two heat baths (described by wave equations). Assuming that theâ€¦ (More)

The primary objective of this work is to develop coarse-graining schemes for stochas-tic many-body microscopic models and quantify their effectiveness in terms of a priori and a pos-teriori errorâ€¦ (More)

We present a selective overview of the current state of our knowledge (more precisely of our ignorance) regarding the derivation of Fourier's Law, J(r) = âˆ’Îºâˆ‡T (r); J the heat flux, T the temperatureâ€¦ (More)

We give large deviation upper bounds, and discuss lower bounds, for the Gibbs-KMS state of a system of quantum spins or an interacting Fermi gas on the lattice. We cover general interactions andâ€¦ (More)

In these notes we discuss Markov processes, in particular stochastic differential equations (SDE) and develop some tools to analyze their long-time behavior. There are several ways to analyze suchâ€¦ (More)

We consider a finite chain of non-linear oscillators coupled at its ends to two infinite heat baths which are at different temperatures. Using our earlier results about the existence of a stationaryâ€¦ (More)

We prove large deviation principles for ergodic averages of dynamical systems admitting Markov tower extensions with exponential return times. Our main technical result from which a number of limitâ€¦ (More)

We consider a model of heat conduction introduced in [6], which consists of a finite nonlinear chain coupled to two heat reservoirs at different temperatures. We study the low temperature asymptoticâ€¦ (More)

Within the abstract framework of dynamical system theory we describe a general approach to the Transient (or Evans-Searles) and Steady State (or Gallavotti-Cohen) Fluctuation Theorems ofâ€¦ (More)

We use the low-temperature expansion and the extension of Pirogov-Sinai theory developed in [1], and the perturbation theory of [2] to describe the phase diagrams of two families of fermionic latticeâ€¦ (More)