Towards a complete theory of quantum thermodynamics

Extending the formalism of thermodynamics to apply to small quantum systems away from thermal equilibrium is a program that has received much interest recently. However, we still have a very limited understanding of how quantum coherence between different energy levels evolves under thermodynamic processes. Quantum coherence is especially important in exotic and useful low-temperature phenomena such as superconductivity and magnetic reso- nance. In this talk we report an novel characterization of thermodynamic processes in the low-temperature regime. Calling the resulting mathematical model ”cooling maps”, we present necessary and sufficient conditions for the fea- sibility of state transitions under cooling maps, including the transformation of coherence. We also present an explicit construction of low-temperature thermodynamic processes that preserve coherence to the maximum extent possible. While other recent works have provided important insights into the workings of quantum coherence in thermodynam- ics, our treatment enables us to find elegant and succinct conditions in the low-temperature regime. Combining the spirit of our approach with that of other works could pave the way towards a more complete understanding of coherent thermodynamics at general temperatures. Based on our article (to appear in Nature Communications).