  Fluctuations of the work performed on a driven quantum system can be
characterized by the so-called fluctuation theorems. The Jarzynski relation and
the Crooks theorem are famous examples of exact equalities characterizing
non-equilibrium dynamics. Such statistical theorems are typically formulated in
a similar manner in both classical and quantum physics. Leggett-Garg
inequalities are inspired by the two assumptions referred to as the macroscopic
realism and the non-invasive measurability. Together, these assumptions are
known as the macrorealism in the broad sense. Quantum mechanics is provably
incompatible with restrictions of the Leggett-Garg type. It turned out that
Leggett-Garg inequalities can be used to distinguish quantum and classical work
fluctuations. We develop this issue with the use of entropic functions of the
Tsallis type. Varying the entropic parameter, we are often able to reach more
robust detection of violations of the corresponding Leggett-Garg inequalities.
In reality, all measurement devices suffer from losses. Within the entropic
formulation, detection inefficiencies can naturally be incorporated into the
consideration. This question also shows advantages that are provided due to the
use of generalized entropies.
