Thermodynamics of Quantum Information Systems — Hamiltonian Description

It is often claimed, that from a quantum system of d levels, and entropy S and heat bath of temperature T one can draw kT lnd–TS amount of work. However, the usual arguments basing on Szilard engine, are not fully rigorous. Here we prove the formula within Hamiltonian description of drawing work from a quantum system and a heat bath, at the cost of entropy of the system. We base on the derivation of thermodynamical laws and quantities in 10 within weak coupling limit. Our result provides fully physical scenario for extracting thermodynamical work form quantum correlations 4. We also derive Landauer's principle as a consequence of the second law within the considered model.