Journal of Statistical Physics

, Volume 78, Issue 1, pp 463–494

Criteria for local equilibrium in a system with transport of heat and mass

  • Bjørn Hafskjold
  • Signe Kjelstrup Ratkje

DOI: 10.1007/BF02183360

Cite this article as:
Hafskjold, B. & Ratkje, S.K. J Stat Phys (1995) 78: 463. doi:10.1007/BF02183360


Nonequilibrium molecular dynamics is used to compute the coupled heat and mass transport in a binary isotope mixture of particles interacting with a Lennard-Jones/spline potential. Two different stationary states are studied, one with a fixed internal energy flux and zero mass flux, and the other with a fixed diffusive mass flux and zero temperature gradient. Computations are made for one overall temperature,T=2, and three overall number densities,n=0.1, 0.2, and 0.4. (All numerical values are given in reduced, Lennard-Jones units unless otherwise stated.) Temperature gradients are up to ∇T=0.09 and weight-fraction gradients up to ∇w1=0.007. The flux-force relationships are found to be linear over the entire range. All four transport coefficients (theL-matrix) are determined and the Onsager reciprocal relationship for the off-diagonal coefficients is verified. Four different criteria are used to analyze the concept of local equilibrium in the nonequilibrium system. The local temperature fluctuation is found to be δT≈0.03T and of the same order as the maximum temperature difference across the control volume, except near the cold boundary. A comparison of the local potential energy, enthalpy, and pressure with the corresponding equilibrium values at the same temperature, density, and composition also verifies that local equilibrium is established, except near the boundaries of the system. The velocity contribution to the BoltzmannH-function agrees with its Maxwellian (equilibrium) value within 1%, except near the boundaries, where the deviation is up to 4%. Our results do not support the Eyring-type transport theory involving jumps across energy barriers; we find that its estimates for the heat and mass fluxes are wrong by at least one order of magnitude.

Key Words

Nonequilibrium molecular dynamicsirreversible thermodynamicsOnsager reciprocal relationslocal equilibrium

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Bjørn Hafskjold
    • 1
  • Signe Kjelstrup Ratkje
    • 1
  1. 1.Department of Physical ChemistryUniversity of Trondheim, Norwegian Institute of TechnologyTrondheimNorway