Nonequilibrium Statistical Mechanics of Classical Lattice φ4 Field Theory

Abstract

We study the nonequilibrium statistical mechanics of classical lattice φ 4 theory in thermal gradients of arbitrary strength. The steady-state physics of the theory in (1 + 1) dimensions is investigated from first principles and classified into dynamical regimes. The bulk properties associated with thermal transport are derived. Starting with thermal equilibrium, we examine the relation to the kinetic theory description of the behavior of the system. Green-Kubo transport coefficients are computed and compared to measured transport near and far from equilibrium, defining the scope of linear response and including an analysis of long-time tails. Local equilibrium is investigated and seen to explicitly break down under sufficiently strong gradients. Additional measures of the nonequilibrium steady state are also discussed as well as the connections to irreversible thermodynamics. C 2002 Elsevier Science (USA)

Nonequilibrium statistical mechanics of anharmonic crystals with self-consistent stochastic reservoirs

“…The existence of steady states is proved in [4], and the positivity of entropy production in [5]. Numerical results strongly suggest that the Fourier's law holds in such a case [6], [7], but, in the opposite direction, a perturbative analysis [8] shows that the heat current does not depend on the size of the system. Also in the perturbative study [8], as in harmonic case [3], the temperature profile (discarding the exponential decay in the bulk of the chain) is in the "wrong" way: the hottest temperature is near the coldest bath, and vice-versa.…”

Energy Transport in Weakly Anharmonic Chains

“…The particular case λ = 1, δ = 1 2 is studied in great detail in [16], in which case kinetic theory is applicable at low temperatures. For our purposes it is of importance to add the extra parameter δ, since it is retained in the kinetic limit.…”

“…The speed of phonon propagation can also be measured directly from the time and space dependences of the autocorrelation function J 0,1 (0)J j,j+1 (t) in thermal equilibrium [9,16]. The velocity of the peaks in the correlation function is equated with the average phonon velocity relevant for thermal transport.…”

Non-equilibrium Statistical Mechanics of Classical and Quantum Systems

“…The boundary conditions can be implemented in a variety of ways [3]. Before we discuss quantum systems, we present some results for classical systems, which summarizes results in Refs.…”

“…Before we discuss quantum systems, we present some results for classical systems, which summarizes results in Refs. [3]- [8] and references there in.…”