Non-Markovian quantum thermodynamics: laws and fluctuation theorems

TL;DR

This paper integrates Keldysh non-equilibrium quantum theory with thermodynamics, establishing that quantum fluctuation theorems hold for non-Markovian systems and are consistent with classical results, regardless of initial states or approximations.

Contribution

It demonstrates the equivalence of real-time diagrammatic techniques to stochastic thermodynamics for non-Markovian quantum systems and derives quantum fluctuation theorems applicable to various initial states and approximations.

Findings

Quantum fluctuation theorems hold for non-Markovian systems.

Symmetries between quantum trajectories and their reverses are established.

Fluctuation theorems are valid for initial states with non-factorizable correlations.

Abstract

This work brings together Keldysh non-equilibrium quantum theory and thermodynamics, by showing that a real-time diagrammatic technique 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 non-factorizable initial states. The sequential tunnelling approximation and the cotunnelling 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 ensures that the second law of thermodynamics holds on average, even if fluctuations violate it. [ERRATUM added: March 2021]