Related Experiment Video
Updated: May 16, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Dynamical equations for time-ordered Green's functions: from the Keldysh time-loop contour to equilibrium at finite
1Department of Physics, University of York, Heslington, York, UK. herve.ness@york.ac.uk
Abstract:
We study the dynamical equation of the time-ordered Green's function at finite temperature. We show that the time-ordered Green's function obeys a conventional Dyson equation only at equilibrium and in the limit of zero temperature. In all other cases, i.e. finite temperature at equilibrium or non-equilibrium, the time-ordered Green's function obeys instead a modified Dyson equation. The derivation of this result is obtained from the general formalism of the non-equilibrium Green's functions on the Keldysh time-loop contour. At equilibrium, our result is fully consistent with the Matsubara temperature Green's function formalism and also justifies rigorously the correction terms introduced in an ad hoc way with Hedin and Lundqvist. Our results show that one should use the appropriate dynamical equation for the time-ordered Green's function when working beyond the equilibrium zero-temperature limit.
Related Concept Videos
Free Energy and Equilibrium
Recall that Q is the numerical value of the mass action expression...
Free Energy and Equilibrium
The reaction quotient, Q, is a convenient measure of the status of an...
Separable Differential Equations
Dynamic Equilibrium
Zeroth Law of Thermodynamics
The Zeroth Law of Thermodynamics
