Boltzmann subspaces in molecular junctions under a thermal bias

Single molecule junctions enable us to study molecules in new states far from equilibrium. In this work, we focus on molecules under a thermal bias imposed by coupling to two electrodes at different temperatures. We demonstrate that within the realm of weak electrode-molecule coupling (Pauli master equations), even far from equilibrium, the molecule can be assigned (at least approximately) an effective temperature at steady state. This is manifested in clustering of the molecular Hamiltonian eigenstates into groups with Boltzmann distributions of occupation probabilities. We demonstrate the emergence of such Boltzmann subspaces under thermal bias and identify the corresponding effective temperature in a variety of molecular junction models, including account for electron-electron interaction, molecular disorder, asymmetric coupling to the electrodes, and the orbital energy density. The results are promising from a practical perspective as we draw guidelines for controlling the temperature of single-molecule electronic devices. The existence of Boltzmann subspaces simplifies our understanding of transport in open quantum systems under thermal bias and holds promise for reducing the numerical effort in simulations of thermally driven molecular junctions.