Non-Markovian quantum thermodynamics: laws and fluctuation theorems
Résumé
This work brings together thermodynamics and nonequilibrium quantum theory, by showing that a real-time diagrammatic technique on the Keldysh contour is an equivalent of stochastic thermodynamics for non-Markovian quantum machines (heat engines, refrigerators, etc.). Symmetries are found between quantum trajectories and their time reverses on the Keldysh contour, for any interacting quantum system coupled to ideal reservoirs of electrons, phonons, or photons. These lead to quantum fluctuation theorems the same as the well-known classical ones (Jarzynski and Crooks equalities, integral fluctuation theorem, etc.), whether the system's dynamics are Markovian or not. Some of these are also shown to hold for nonfactorizable initial states. The sequential tunneling approximation and the cotunneling approximation are both shown to respect the symmetries that ensure the fluctuation theorems. For all initial states, energy conservation ensures that the first law of thermodynamics holds on average, while the above symmetries ensure that the second law of thermodynamics holds on average, even if fluctuations violate it.