  In this paper we derive an explicit formula for the heat kernel of the
asymmetric quantum Rabi model (AQRM), a symmetry breaking generalization of the
quantum Rabi model (QRM). The method described here is an extension of the
recently developed one for the heat kernel of the QRM based on the Trotter-Kato
formula. In particular, the method is not based on path integrals or stochastic
methods. In addition to the heat kernel formula, we present applications
including the explicit formula for the partition function and the Weyl law for
the distribution of the eigenvalues, obtained from the analytic continuation of
the corresponding spectral zeta function.
