Dynamical contribution to the heat conductivity in stochastic energy exchanges of locally confined gases. (24th April 2017)

• Record Type: Journal Article
• Authors: Gaspard, Pierre; Gilbert, Thomas
• Is Part Of: Journal of statistical mechanics. (2017:Apr.)
• Publication Date: 2017-04-24
• Subjects: 4 -- 12; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aa60ce
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We present a systematic computation of the heat conductivity of the Markov jump process modeling the energy exchanges in an array of locally confined hard spheres at the conduction threshold. Based on a variational formula (Sasada 2016 (arXiv:1611.08866)), explicit upper bounds on the conductivity are derived, which exhibit a rapid power-law convergence towards an asymptotic value. We thereby conclude that the ratio of the heat conductivity to the energy exchange frequency deviates from its static contribution by a small negative correction, its dynamic contribution, evaluated to be − 0.000 373 in dimensionless units. This prediction is corroborated by kinetic Monte Carlo simulations which were substantially improved compared to earlier results.