sarkas.tools.observables.Thermodynamics.compute_from_rdf
sarkas.tools.observables.Thermodynamics.compute_from_rdf#
- Thermodynamics.compute_from_rdf(rdf, potential)[source]#
Calculate the correlational energy and correlation pressure using
sarkas.tools.observables.RadialDistributionFunction.compute_sum_rule_integrals()method.The Hartree and correlational terms between species \(A\) and \(B\) are
\[U_{AB}^{\rm hartree} = 2 \pi \frac{N_iN_j}{V} \int_0^\infty dr \, \phi_{AB}(r) r^2 dr,\]\[U_{AB}^{\rm corr} = 2 \pi \frac{N_iN_j}{V} \int_0^\infty dr \, \phi_{AB}(r) h(r) r^2 dr,\]\[P_{AB}^{\rm hartree} = - \frac{2 \pi}{3} \frac{N_iN_j}{V^2} \int_0^\infty dr \, \frac{d\phi_{AB}(r)}{dr} r^3 dr,\]\[P_{AB}^{\rm corr} = - \frac{2 \pi}{3} \frac{N_iN_j}{V^2} \int_0^\infty dr \, \frac{d\phi_{AB}(r)}{dr} h(r) r^3 dr,\]- Parameters
rdf (sarkas.tools.observables.RadialDistributionFunction) – Radial Distribution Function object.
potential (
sarkas.potentials.core.Potential) – Potential object.
- Returns
nkT (float) – Ideal term of the pressure \(nk_BT\). Where \(n\) is the total density.
u_hartree (numpy.ndarray) – Hartree energy calculated from the above formula for each \(g_{ab}(r)\).
u_corr (numpy.ndarray) – Correlational energy calculated from the above formula for each \(g_{ab}(r)\).
p_hartree (numpy.ndarray) – Hartree pressure calculated from the above formula for each \(g_{ab}(r)\).
p_corr (numpy.ndarray) – Correlational pressure calculated from the above formula for each \(g_{ab}(r)\).