Duality and exact correlations for a model of heat conduction
arXiv:cond-mat/0612198 · doi:10.1063/1.2711373
Abstract
We study a model of heat conduction with stochastic diffusion of energy. We obtain a dual particle process which describes the evolution of all the correlation functions. An exact expression for the covariance of the energy exhibits long-range correlations in the presence of a current. We discuss the formal connection of this model with the simple symmetric exclusion process.
19 pages
Cited by in corpus (59)
- Macroscopic fluctuation theory
- Duality and hidden symmetries in interacting particle systems
- Mapping out of equilibrium into equilibrium in one-dimensional transport models
- Master equations and the theory of stochastic path integrals
- Duality for stochastic models of transport
- Condensation in the inclusion process and related models
- Fluctuating hydrodynamics, current fluctuations and hyperuniformity in boundary-driven open quantum chains
- A stochastic model of anomalous heat transport: analytical solution of the steady state
- Dynamics of condensation in the symmetric inclusion process
- Equilibrium-like fluctuations in some boundary-driven open diffusive systems
- Condensation in stochastic mass transport models: beyond the zero-range process
- Metastability in the reversible inclusion process
- Nonequilibrium dynamics of a stochastic model of anomalous heat transport
- Self-Duality for the Two-Component Asymmetric Simple Exclusion Process
- Asymmetric stochastic transport models with symmetry
- Dynamics of condensation in the totally asymmetric inclusion process
- Fourier's law from a chain of coupled planar harmonic oscillators under energy conserving noise
- Non-compact quantum spin chains as integrable stochastic particle processes
- Large Deviations in Stochastic Heat-Conduction Processes Provide a Gradient-Flow Structure for Heat Conduction
- Duality and hidden equilibrium in transport models
- Nonequilibrium Invariant Measure under Heat Flow
- Duality in interacting particle systems and boson representation
- Orthogonal Dualities of Markov Processes and Unitary Symmetries
- Orthogonal stochastic duality functions from Lie algebra representations
- Self-duality of Markov processes and intertwining functions
- Fluctuations in interacting particle systems with memory
- Extended duality relations between birth-death processes and partial differential equations
- Symmetric inclusion process with slow boundary: hydrodynamics and hydrostatics
- The kinetic exclusion process: a tale of two fields
- Structure of the condensed phase in the inclusion process
- Superdiffusivity of Asymmetric Energy Model in Dimension One and Two
- On dualities for SSEP and ASEP with open boundary conditions
- Integrable stochastic dualities and the deformed Knizhnik-Zamolodchikov equation
- Explosive condensation in symmetric mass transport models
- Integrable heat conduction model
- Extreme current fluctuations of boundary-driven systems in the large-N limit
- Duality in stochastic processes from the viewpoint of basis expansions
- Weakly Non-Equilibrium Properties of Symmetric Inclusion Process with Open Boundaries
- Approximate filtering via discrete dual processes
- Markov duality and Bethe ansatz formula for half-line open ASEP
- Duality in quantum transport models
- Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations
- Weak coupling limits in a stochastic model of heat conduction
- A Unified Interface Model for Dissipative Transport of Bosons and Fermions
- Making Birth-Death Processes from Backward Fokker-Planck Equations for Computing Expectations in Langevin Systems
- Size-biased diffusion limits and the inclusion process
- Orthogonal Intertwiners for Infinite Particle Systems in The Continuum
- Transport-induced correlations in weakly interacting systems
- Poisson-Dirichlet asymptotics in condensing particle systems
- Conservative interacting particles system with anomalous rate of ergodicity
- Stochastic duality and eigenfunctions
- Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
- Heat conduction and the nonequilibrium stationary states of stochastic energy exchange processes
- Representations of the current algebra and probabilistic perspectives
- Dual process in the two-parameter Poisson-Dirichlet diffusion
- Nonequilibrium Microscopic Distribution of Thermal Current in Particle Systems
- Spectral gap of the symmetric inclusion process
- Redundant basis interpretation of Doi-Peliti method and an application
- A stochastic model solvable without integrability