Fluctuation theorem for nonunital dynamics

We derive an expression for the fluctuations of energy in open quantum system undergoing a nontrivial evolution. The statistics are constructed by means two-point measurement process when has been evolved completely positive and trace-preserving map. depend only on state dynamical map generating In particular, we consider Tasaki–Crooks fluctuation theorem, where unitary evolution is replaced channel. Our construction backward using ancilla sheds important light mathematical structure at play nonunital channels considered thermodynamics.