Heat conduction and the nonequilibrium stationary states of stochastic energy exchange processes

Abstract

I revisit the exactly solvable Kipnis--Marchioro--Presutti model of heat conduction [J. Stat. Phys. 27 65 (1982)] and describe, for one-dimensional systems of arbitrary sizes whose ends are in contact with thermal baths at different temperatures, a systematic characterization of their non-equilibrium stationary states. These arguments avoid resorting to the analysis of a dual process and yield a straightforward derivation of Fourier's law, as well as higher-order static correlations, such as the covariant matrix. The transposition of these results to families of gradient models generalizing the KMP model is established and specific cases are examined.

26 pages

References in corpus (6)

• Duality and hidden symmetries in interacting particle systems
• Asymmetric stochastic transport models with ${\mathcal{U}}_q(\mathfrak{su}(1,1))$ symmetry
• Large Deviations in Stochastic Heat-Conduction Processes Provide a Gradient-Flow Structure for Heat Conduction
• Duality and stationary distributions of the "Immediate Exchange Model" and its generalizations
• Local equilibrium in inhomogeneous stochastic models of heat transport
• Multilinearity of two-point correlation functions in one-dimensional models out of equilibrium

Cited by in corpus (2)

• Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations
• Quasi-potentials in the Nonequilibrium Stationary States or a method to get explicit solutions of Hamilton-Jacobi equations