Non-Equilibrium Statistical Mechanics of Classical Lattice ${\varphi }^4$ Field Theory

Abstract

Classical ${\varphi }^4$ theory in weak and strong thermal gradients is studied on the lattice in (1+1) dimensions. Classical ${\varphi }^4$ theory in weak and strong thermal gradients is studied on the lattice in (1+1) dimensions. The steady state physics of the theory is investigated from first principles and classified into dynamical regimes. We derive the bulk properties associated with thermal transport, and explore in detail the non-equilibrium statistical mechanics of the theory as well as connections to equilibrium and irreversible thermodynamics. Linear response predictions are found to be valid for systems quite far from equilibrium and are seen to eventually break down simultaneously with local equilibrium.

28 pages, 20 figs

References in corpus (3)

• Bulk Properties of Anharmonic Chains in Strong Thermal Gradients: Non-Equilibrium ${\varphi }^4$ Theory
• FPU $\beta$ model: Boundary Jumps, Fourier's Law and Scaling
• Non-Equilibrium Steady States and Transport in the Classical Lattice ${\varphi }^4$ Theory

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• Normal Heat Conductivity in a strongly pinned chain of anharmonic oscillators
• Fourier's Law from Closure Equations
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• Violations of local equilibrium and linear response in classical lattice theories
• Pressure-induced recovery of Fourier's law in one dimensional momentum-conserving systems
• Thermal rectification in anharmonic chains under an energy-conserving noise
• One-dimensional Superdiffusive Heat Propagation Induced by Optical Phonon-Phonon Interactions
• Numerical examination of steady-state thermodynamics from the entropy connected to the excess heat
• Perturbative analysis of anharmonic chains of oscillators out of equilibrium
• Stable and unstable periodic orbits in the one dimensional lattice ${\varphi }^4$ theory
• Comment on "Logarithmic Oscillators: Ideal Hamiltonian Thermostats" [arXiv 1203.5968]
• On the derivation of Fourier's law for coupled anharmonic oscillators
• Heat pump without particle transport or external work on the medium achieved by differential thermostatting of the phase space
• On the Boltzmann Equation for Weakly Nonlinear Wave Equations
• Projective-truncation-approximation study of the one-dimensional ${\varphi }^4$ lattice model
• Heat flow in anharmonic crystals with internal and external stochastic baths: A convergent polymer expansion for a model with discrete time and long range interparticle interaction
• Systematic study of the completeness of two-dimensional classical ${\varphi }^4$ theory
• A Symmetry Property of Momentum Distribution Functions in the Nonequilibrium Steady State of Lattice Thermal Conduction
• Violations of local equilibrium and stochastic thermostats
• Dephasing enhanced transport in boundary-driven quasiperiodic chains