  In recent times the possibility of non-reciprocity in heat transfer between
two bodies has been extensively studied. In particular the role of strong
magnetic fields has been investigated. A much simpler approach with
considerable flexibility would be to consider heat transfer in synthetic
electric and magnetic fields which are easily applied. We demonstrate the
breakdown of detailed balance for the heat transfer function $\mathcal{T}
({\omega})$, i.e. the spectrum of heat transfer between two objects due to the
presence of synthetic electric and magnetic fields. The spectral measurements
carry lot more physical information and were the reason for the quantum theory
of radiation. We demonstrate explicitly the synthetic field induced
non-reciprocity in the heat transfer transmission function between two graphene
flakes and for the Casimir coupling between two objects. Unlike many other
cases of heat transfer, the latter case has interesting features of the strong
coupling. Further the presence of synthetic fields affects the mean occupation
numbers of two membranes and propose this system for the experimental
verification of the breakdown of detailed balance.
