QUANTUM FLUCTUATION THEOREM IN THE EXISTENCE OF THE TUNNELING AND THE THERMAL ACTIVATION

We explore the fluctuation theorem for a diffusion in a tilted washboard potential where both the quantum tunneling and the thermal activation play a role. The diffusion process is treated as a biased random walk where the transition rates are enhanced due to the quantum tunneling. Within this framework, the dissipation is easy to handle, since we need not to measure the experimentally inaccessible quantity like total Hamiltonian which includes the bath degrees of freedom.