The Flow of Heat and Entropy in the Quantum Limit

The dissipation of heat is an inevitable byproduct of all processes, be they physical, chemical, biological, or computational, putting fundamental limits on the energy required. For quantum machines, these limits have heretofore appeared almost prohibitively stringent due to the large entropy produced in processes at low absolute temperatures. However, we show that the conventional formulas used to compute heat and entropy produced in quantum processes are incomplete as they omit a term involving the flow of free energy that becomes increasingly important at low temperatures. We analyze both steady-state and transient flows of heat and entropy in three representative driven quantum systems, and show that inclusion of the new term is needed to obey the 3rd Law of Thermodynamics. Importantly, the correct results for heat dissipated in quantum processes are orders of magnitude less than that predicted by the conventional formula. The crossover to the macroscopic limit, where the conventional formula is recovered, is demonstrated.