Recent advances in experimental techniques allow one to measure and control
systems at the level of single molecules and atoms. Here gaining information
about fluctuating thermodynamic quantities is crucial for understanding
nonequilibrium thermodynamic behavior of small systems. To achieve this aim,
stochastic thermodynamics offers a theoretical framework, and nonequilibrium
equalities such as Jarzynski equality and fluctuation theorems provide key
information about the fluctuating thermodynamic quantities. We review the
recent progress in quantum fluctuation theorems, including the studies of
Maxwell's demon which plays a crucial role in connecting thermodynamics with
information.Comment: As a chapter of: F. Binder, L. A. Correa, C. Gogolin, J. Anders, and
G. Adesso (eds.), "Thermodynamics in the quantum regime - Fundamental Aspects
and New Directions", (Springer International Publishing, 2018