onsager.out

This file contains some components of the running onsager coefficients tensor from the homogeneous non-equilibrium molecular dynamics Evans-Cummings algorithm (HNEMDEC) method. It is generated when invoking the compute_hnemdec keyword.

File format

If the driving force is in the \(\mu\) (\(\mu\) can be \(x\), \(y\), or \(z\)) direction and the dissipative flux is set as heat flux, for a system with \(M\) elements, this file reads:

  • column 1: \(L_{x \mu}^{\text{qq}}(t)\) (in units of \(W/mK\))

  • column 2: \(L_{y \mu}^{\text{qq}}(t)\) (in units of \(W/mK\))

  • column 3: \(L_{z \mu}^{\text{qq}}(t)\) (in units of \(W/mK\))

  • column 4: \(L_{x \mu}^{\text{1q}}(t)\) (in units of \(10^{-6} kg/smK\))

  • column 5: \(L_{y \mu}^{\text{1q}}(t)\) (in units of \(10^{-6} kg/s/m/K\))

  • column 6: \(L_{z \mu}^{\text{1q}}(t)\) (in units of \(10^{-6} kg/s/m/K\))

  • …

  • column 3M+1: \(L_{x \mu}^{\text{Mq}}(t)\) (in units of \(10^{-6} kg/smK\))

  • column 3M+2: \(L_{y \mu}^{\text{Mq}}(t)\) (in units of \(10^{-6} kg/smK\))

  • column 3M+3: \(L_{z \mu}^{\text{Mq}}(t)\) (in units of \(10^{-6} kg/smK\))

If the dissipative flux is changed to momentum flux of component \(\alpha\), this file reads:

  • column 1: \(L_{x \mu}^{q\alpha}(t)\) (in units of \(10^{-6} kg/smK\))

  • column 2: \(L_{y \mu}^{q\alpha}(t)\) (in units of \(10^{-6} kg/smK\))

  • column 3: \(L_{z \mu}^{q\alpha}(t)\) (in units of \(10^{-6} kg/smK\))

  • column 4: \(L_{x \mu}^{1\alpha}(t)\) (in units of \(10^{-12} kgs/m^{3}K\))

  • column 5: \(L_{y \mu}^{1\alpha}(t)\) (in units of \(10^{-12} kgs/m^{3}K\))

  • column 6: \(L_{z \mu}^{1\alpha}(t)\) (in units of \(10^{-12} kgs/m^{3}K\))

  • …

  • column \(3M+1\): \(L_{x \mu}^{M\alpha}(t)\) (in units of \(10^{-12} kgs/m^{3}K\))

  • column \(3M+2\): \(L_{y \mu}^{M\alpha}(t)\) (in units of \(10^{-12} kgs/m^{3}K\))

  • column \(3M+3\): \(L_{z \mu}^{M\alpha}(t)\) (in units of \(10^{-12} kgs/m^{3}K\))

Both the potential part and the kinetic part of the heat current have been considered. One can obtain the onsager coefficent \(\Lambda_{i j}^{ml}\) by:

\[\Lambda_{i j}^{ml}=T^{2}L_{i j}^{ml}\]

The thermal conductivity can be derived from the onsager matrix \(\Lambda\), that is:

\[\kappa=\frac{1}{T^{2}(\Lambda^{-1})_{00}}\]