Non-Markovian Quantum Heat Statistics with the Reaction Coordinate Mapping

The definition of heat in quantum mechanics is ambiguous. Complications arise in particular when the coupling between a quantum system and a thermal environment is non-negligible, as the boundary between the two becomes blurred, making the distinction between system and environment difficult to draw. The reaction coordinate mapping can be used in such regimes to redraw the boundary between the system and environment. In this paper we combine the reaction coordinate technique with a two-point measurement protocol to compare two different definitions of heat: energetic changes with respect to the full environment Hamiltonian (prior to the mapping), and energetic changes with respect to the residual environment Hamiltonian (after the mapping). We find that the latter definition displays behaviour more expected of a heat bath in the highly non-Markovian regime considered.