  In this chapter we address the topic of quantum thermodynamics in the
presence of additional observables beyond the energy of the system. In
particular we discuss the special role that the generalized Gibbs ensemble
plays in this theory, and derive this state from the perspectives of a
micro-canonical ensemble, dynamical typicality and a resource-theory
formulation. A notable obstacle occurs when some of the observables do not
commute, and so it is impossible for the observables to simultaneously take on
sharp microscopic values. We show how this can be circumvented, discuss
information-theoretic aspects of the setting, and explain how thermodynamic
costs can be traded between the different observables. Finally, we discuss open
problems and future directions for the topic.
