Fluctuation theorems for quantum master equations

A quantum fluctuation theorem for a driven quantum subsystem interacting with its environment is derived based solely on the assumption that its reduced density matrix obeys a closed evolution equation—i.e., a quantum master equation (QME). Quantum trajectories and their associated entropy, heat, and work appear naturally by transforming the QME to a time-dependent Liouville space basis that diagonalizes the instantaneous reduced density matrix of the subsystem. A quantum integral fluctuation theorem, a steady-state fluctuation theorem, and the Jarzynski relation are derived in a similar way as for classical stochastic dynamics.

Figure 1

Representation of a quantum forward trajectory $n_{\left(\tau \right)}$ and of the associated backward trajectory ${\tilde{n}}_{\left(\tilde{\tau }\right)}$.