Thermodynamics of a stochastic three level elevator model

We study the thermodynamic properties of a single particle occupying one of three available energy levels in a non-equilibrium regime. The particle is thermally coupled to a classical Maxwell-Boltzmann thermal reservoir and can jump among the available levels by exchanging energy with the heat bath. The bottom and middle energy levels are simultaneously raised at a given rate regardless of particle occupation, but keeping the energy gaps among the three levels fixed. We explicitly calculate the work, heat and entropy production rates, and the classical efficiency. We also consider the case of a Bose-Einstein thermal reservoir and provide explicit expressions for the non-equilibrium, steady-state probabilities.