  The equilibrium state of a quantum system can deviate from the Gibbs state if
the system-environment coupling is not weak. An analytical expression for this
mean force Gibbs state (MFGS) is known in the ultrastrong coupling (USC) regime
for the Caldeira-Leggett (CL) model that assumes a harmonic environment. Here,
we derive analytical expressions for the MFGS in the USC regime for more
general system-environment models. For all the generalized models considered
here, we find the USC state to be diagonal in the basis set by the
system-environment interaction, just like in the CL case. While for the generic
model considered, the corresponding USC-MFGS state is found to alter from the
CL-result, we do identify a class of models more general than the CL-model for
which the CL-USC result remains unchanged. We also provide numerical
verification for our results. These results provide key tools for the study of
strong coupling thermodynamics under more realistic system-environment models,
going beyond the CL-model.
