Results 1 
3 of
3
NonEquilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures
, 1999
"... . We study the statistical mechanics of a finitedimensional nonlinear Hamiltonian system (a chain of anharmonic oscillators) coupled to two heat baths (described by wave equations). Assuming that the initial conditions of the heat baths are distributed according to the Gibbs measures at two differ ..."
Abstract

Cited by 53 (14 self)
 Add to MetaCart
. We study the statistical mechanics of a finitedimensional nonlinear Hamiltonian system (a chain of anharmonic oscillators) coupled to two heat baths (described by wave equations). Assuming that the initial conditions of the heat baths are distributed according to the Gibbs measures at two different temperatures we study the dynamics of the oscillators. Under suitable assumptions on the potential and on the coupling between the chain and the heat baths, we prove the existence of an invariant measure for any temperature difference, i.e., we prove the existence of steady states. Furthermore, if the temperature difference is sufficiently small, we prove that the invariant measure is unique and mixing. In particular, we develop new techniques for proving the existence of invariant measures for random processes on a noncompact phase space. These techniques are based on an extension of the commutator method of H ormander used in the study of hypoelliptic differential operators. 1. Intr...
A GallavottiCohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
 J. STAT. PHYS
, 1999
"... ..."
Stationary nonequilibrium states in boundarydriven Hamiltonian systems
 J. Chem. Phys
, 1997
"... We investigate stationary nonequilibrium states of systems of particles moving according to Hamiltonian dynamics with specified potentials. The systems are driven away from equilibrium by Maxwell demon “reflection rules ” at the walls. These deterministic rules conserve energy but not phase space vo ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
We investigate stationary nonequilibrium states of systems of particles moving according to Hamiltonian dynamics with specified potentials. The systems are driven away from equilibrium by Maxwell demon “reflection rules ” at the walls. These deterministic rules conserve energy but not phase space volume, and the resulting global dynamics may or may not be time reversible (or even invertible). Using rules designed to simulate moving walls we can obtain a stationary shear flow. Assuming that for macroscopic systems this flow satisfies the NavierStokes equations, we compare the hydrodynamic entropy production with the average rate of phase space volume compression. We find that they are equal when the velocity distribution of particles incident on the walls is a local Maxwellian. An argument for a general equality of this kind, based on the assumption of local thermodynamic equilibrium, is given. Molecular dynamic simulations of hard disks in a channel produce a steady shear flow with the predicted behavior. 1