  We extend on ideas from standard thermodynamics to show that temperature can
be assigned to a general nonequilibrium quantum system. By choosing a
physically motivated complete set of observables and expanding the system state
thereupon, one can read a set of relevant, independent thermodynamic variables
which include internal energy. This expansion allows us to read a
nonequilibrium temperature as the partial derivative of the von Neumann entropy
with respect to internal energy. We show that this definition of temperature is
one of a set of thermodynamics parameters unambiguously describing the system
state. It has appealing features such as positivity for passive states and
consistency with the standard temperature for thermal states. By attributing
temperature to correlations in a bipartite system, we obtain a universal
relation which connects the temperatures of subsystems, total system as a
whole, and correlation. All these temperatures can be different even when the
composite system is in a well-defined Gibbsian thermal state.
