  In this article, we compare the results of non-equilibrium (NEMD) and
equilibrium (EMD) molecular dynamics methods to compute the thermal conductance
at the interface between solids. We propose to probe the thermal conductance
using equilibrium simulations measuring the decay of the thermally induced
energy fluctuations of each solid. We also show that NEMD and EMD give
generally speaking inconsistent results for the thermal conductance: Green Kubo
simulations probe the Landauer conductance between two solids which assumes
phonons on both sides of the interface to be at equilibrium. On the other hand,
we show that NEMD give access to the out-of-equilibrium interfacial conductance
consistent with the interfacial flux describing phonon transport in each solid.
The difference may be large and reaches typically a factor 5 for interfaces
between usual semi-conductors. We analyze finite size effects for the two
determinations of the interfacial thermal conductance, and show that the
equilibrium simulations suffer from severe size effects as compared to NEMD. We
also compare the predictions of the two above mentioned methods -EMD and NEMD-
regarding the interfacial conductance of a series of mass mismatched
Lennard-Jones solids. We show that the Kapitza conductance obtained with EMD
can be well described using the classical diffuse mismatch model (DMM). On the
other hand, NEMD simulations results are consistent with a out-of-equilibrium
generalisation of the acoustic mismatch model (AMM). These considerations are
important in rationalizing previous results obtained using molecular dynamics,
and help in pinpointing the physical scattering mechanisms taking place at
atomically perfect interfaces between solids, which is a prerequesite to
understand interfacial heat transfer across real interfaces.
