  Given the algebra of observables of a quantum system subject to selection
rules, a state can be represented by different density matrices. As a result,
different von Neumann entropies can be associated with the same state.
Motivated by a minimality property of the von Neumann entropy of a density
matrix with respect to its possible decompositions into pure states, we give a
purely algebraic definition of entropy for states of an algebra of observables,
thus solving the above ambiguity. The entropy so defined satisfies all the
desirable thermodynamic properties, and reduces to the von Neumann entropy in
the quantum mechanical case. Moreover, it can be shown to be equal to the von
Neumann entropy of the unique representative density matrix belonging to the
operator algebra of a multiplicity-free Hilbert-space representation.
