  A general tool for description of open quantum systems is given by the
formalism of quantum operations. Most important of them are trace-preserving
maps also known as quantum channels. We discuss those conditions on quantum
channels under which the Jarzynski equality and related fluctuation theorems
hold. It is essential that the representing quantum channel be unital. Under
the mentioned condition, we first derive the corresponding Jarzynski equality.
For bistochastic map and its adjoint, we further formulate a theorem of
Tasaki-Crooks type. In the context of unital channels, some notes on heat
transfer between two quantum systems are given. We also consider the case of a
finite system operated by an external agent with a feedback control. When
unital channels are applied at the first stage and, for a mutual-information
form, at the further ones, we obtain quantum Jarzynski-Sagawa-Ueda relations.
These are extension of the previously given results to unital quantum
operations.
